The name Indianapolis is derived from the state's name, Indiana (meaning "Land of the Indians", or simply "Indian Land"), and polis, the Greek word for "city." Jeremiah Sullivan, justice of the Indiana Supreme Court, is credited with coining the name. Other names considered were Concord, Suwarrow, and Tecumseh.

In 1816, the year Indiana gained statehood, the U.S. Congress donated four sections of federal land to establish a permanent seat of state government. Two years later, under the Treaty of St. Mary's (1818), the Delaware relinquished title to their tribal lands in central Indiana, agreeing to leave the area by 1821. This tract of land, which was called the New Purchase, included the site selected for the new state capital in 1820. The indigenous people of the land prior to systematic removal are the Miami Nation of Indiana (Miami Nation of Oklahoma) and Indianapolis makes up part of Cession 99; the primary treaty between the indigenous population and the United States was the Treaty of St. Mary's (1818).

The availability of new federal lands for purchase in central Indiana attracted settlers, many of them descendants of families from northwestern Europe. Although many of these first European and American settlers were Protestants, a large proportion of the early Irish and German immigrants were Catholics. Few African Americans lived in central Indiana before 1840. The first European Americans to permanently settle in the area that became Indianapolis were either the McCormick or Pogue families. The McCormicks are generally considered to be the first permanent settlers; however, some historians believe George Pogue and family may have arrived first, on March 2, 1819, and settled in a log cabin along the creek that was later called Pogue's Run. Other historians have argued as early as 1822 that John Wesley McCormick, his family, and employees became the area's first European American settlers, settling near the White River in February 1820.

On January 11, 1820, the Indiana General Assembly authorized a committee to select a site in central Indiana for the new state capital. The state legislature approved the site, adopting the name Indianapolis on January 6, 1821. In April, Alexander Ralston and Elias Pym Fordham were appointed to survey and design a town plan for the new settlement. Indianapolis became a seat of county government on December 31, 1821, when Marion County, was established. A combined county and town government continued until 1832 when Indianapolis incorporated as a town. Indianapolis became an incorporated city effective March 30, 1847. Samuel Henderson, the city's first mayor, led the new city government, which included a seven-member city council. In 1853, voters approved a new city charter that provided for an elected mayor and a fourteen-member city council. The city charter continued to be revised as Indianapolis expanded. Effective January 1, 1825, the seat of state government moved to Indianapolis from Corydon, Indiana. In addition to state government offices, a U.S. district court was established at Indianapolis in 1825.

Growth occurred with the opening of the National Road through the town in 1827, the first major federally funded highway in the United States. A small segment of the ultimately failed Indiana Central Canal was opened in 1839. The first railroad to serve Indianapolis, the Jeffersonville, Madison and Indianapolis Railroad, began operation in 1847, and subsequent railroad connections fostered growth.Indianapolis Union Station was the first of its kind in the world when it opened in 1853.

During the American Civil War, Indianapolis was mostly loyal to the Union cause. Governor Oliver P. Morton, a major supporter of President Abraham Lincoln, quickly made Indianapolis a rallying place for Union army troops. On February 11, 1861, President-elect Lincoln arrived in the city, en route to Washington, D.C. for his presidential inauguration, marking the first visit from a president-elect in the city's history. On April 16, 1861, the first orders were issued to form Indiana's first regiments and establish Indianapolis as a headquarters for the state's volunteer soldiers. Within a week, more than 12,000 recruits signed up to fight for the Union.

Indianapolis became a major logistics hub during the war, establishing the city as a crucial military base. Between 1860 and 1870, the city's population more than doubled. An estimated 4,000 men from Indianapolis served in 39 regiments, and an estimated 700 died during the war. On May 20, 1863, Union soldiers attempted to disrupt a statewide Democratic convention at Indianapolis, forcing the proceedings to be adjourned, sarcastically referred to as the Battle of Pogue's Run. Fear turned to panic in July 1863, during Morgan's Raid into southern Indiana, but Confederate forces turned east toward Ohio, never reaching Indianapolis. On April 30, 1865, Lincoln's funeral train made a stop at Indianapolis, where an estimated crowd of more than 100,000 people passed the assassinated president's bier at the Indiana Statehouse.

Following the Civil War—and in the wake of the Second Industrial Revolution—Indianapolis experienced tremendous growth and prosperity. In 1880, Indianapolis was the world's third largest pork packing city, after Chicago and Cincinnati, and the second largest railroad center in the United States by 1888. By 1890, the city's population surpassed 100,000. Some of the city's most notable businesses were founded during this period of growth and innovation, including L. S. Ayres (1872), Eli Lilly and Company (1876), Madam C. J. Walker Manufacturing Company (1910), and Allison Transmission (1915). Once home to 60 automakers, Indianapolis rivaled Detroit as a center of automobile manufacturing. The city was an early focus of labor organization. The Indianapolis Street Car Strike of 1913 and subsequent police mutiny and riots led to the creation of the state's earliest labor-protection laws, including a minimum wage, regular work weeks, and improved working conditions. The International Typographical Union and United Mine Workers of America were among several influential labor unions based in the city.

Some of the city's most prominent architectural features and best known historical events date from the turn of the 20th century. The Soldiers' and Sailors' Monument, dedicated on May 15, 1902, would later become the city's unofficial symbol.Ray Harroun won the inaugural running of the Indianapolis 500, held May 30, 1911, at Indianapolis Motor Speedway. Indianapolis was one of the hardest hit cities in the Great Flood of 1913, resulting in five known deaths and the displacement of 7,000 families.

As a stop on the Underground Railroad, Indianapolis had one of the largest black populations in the Northern States, until the Great Migration. Led by D. C. Stephenson, the Indiana Klan became the most powerful political and social organization in Indianapolis from 1921 through 1928, controlling City Council and the Board of School Commissioners, among others. At its height, more than 40% of native-born white males in Indianapolis claimed membership in the Klan. While campaigning in the city in 1968, Robert F. Kennedy delivered one of the most lauded speeches in 20th century American history, following the assassination of civil rights leader Martin Luther King Jr. As in most U.S. cities during the Civil Rights Movement, the city experienced strained race relations. A 1971 federal court decision forcing Indianapolis Public Schools to implement desegregation busing proved controversial.

Under the mayoral administration of Richard Lugar, the city and county governments restructured, consolidating most public services into a new entity called Unigov. The plan removed bureaucratic redundancies, captured increasingly suburbanizing tax revenue, and created a Republican political machine that dominated Indianapolis politics until the 2000s. Unigov went into effect on January 1, 1970, increasing the city's land area by 308.2 square miles (798 km²) and population by 268,366 people. It was the first major city-county consolidation to occur in the United States without a referendum since the creation of the City of Greater New York in 1898.

Amid the changes in government and growth, the city invested in an aggressive strategy to brand Indianapolis as a sports tourism destination, known as the Indianapolis Project. Under the administration of the city's longest-serving mayor, William Hudnut (1976–1992), millions of dollars were poured into sport facilities and public relations campaigns as part of an economic development strategy. The strategy was successful in landing the U.S. Olympic Festival in 1983, securing the 1984 relocation of the NFL Baltimore Colts, and hosting the 1987 Pan American Games.

Economic development initiatives focused on revitalizing the city's downtown continued in the 1990s under the mayoral administration of Stephen Goldsmith. During this period, a number of cultural amenities were completed at White River State Park, the Canal Walk continued development,Circle Centre Mall was completed, and new sports venues (Victory Field and Bankers Life Fieldhouse) were opened. In 1999, several cultural districts were designated to capitalize on cultural assets within historically significant neighborhoods unique to the city's heritage as a means to promote continued economic development.

During the 2000s, the city invested heavily in infrastructure projects, including two of the largest building projects in the city's history: the $1.1 billion Indianapolis International Airport Colonel H. Weir Cook Terminal and $720 million Lucas Oil Stadium, both opened in 2008. A $275 million expansion of the Indiana Convention Center was completed in 2011. Construction began that year on DigIndy, a $1.9 billion project to correct the city's combined sewer overflows by 2025. Rapid transit was reintroduced to Indianapolis with the opening of IndyGo's $96 million Red Line bus rapid transit project in 2019.

The U.S. Census Bureau considers Indianapolis as two entities: the consolidated city and the city's remainder, or balance. The consolidated city is coterminous with Marion County, except the independent municipalities of Beech Grove, Lawrence, Southport, and Speedway. The city's balance excludes the populations of ten semi-autonomous municipalities that are included in totals for the consolidated city. These are Clermont, Crows Nest, Homecroft, Meridian Hills, North Crows Nest, Rocky Ripple, Spring Hill, Warren Park, Williams Creek, and Wynnedale. An eleventh town, Cumberland, is partially included. In 2018 estimates, the city's consolidated population was 876,862 and its balance was 867,125. At the 2010 Census, the city's population density was 2,270 people per square mile (880/km²). Indianapolis is the most populous city in Indiana, containing nearly 13% of the state's total population.

The Indianapolis metropolitan area, officially the Indianapolis–Carmel–Anderson metropolitan statistical area (MSA), consists of Marion County and the surrounding counties of Boone, Brown, Hamilton, Hancock, Hendricks, Johnson, Madison, Morgan, Putnam, and Shelby. In 2018, the metropolitan area's population was 2,048,703, the most populous in Indiana and home to 30% of the state's residents. With a population of 2,431,361, the larger Indianapolis–Carmel–Muncie combined statistical area (CSA) covers 18 counties, home to 36% of Indiana residents. Indianapolis is also situated within the Great Lakes Megalopolis, the largest of 11 megaregions in the U.S.

According to the U.S. Census of 2010, 97.2% of the Indianapolis population was reported as one race: 61.8% White, 27.5% Black or African American, 2.1% Asian (0.4% Burmese, 0.4% Indian, 0.3% Chinese, 0.3% Filipino, 0.1% Korean, 0.1% Vietnamese, 0.1% Japanese, 0.1% Thai, 0.1% other Asian); 0.3% American Indian, and 5.5% as other. The remaining 2.8% of the population was reported as multiracial (two or more races). The city's Hispanic or Latino community comprised 9.4% of the city's population in the 2010 U.S. Census: 6.9% Mexican, 0.4% Puerto Rican, 0.1% Cuban, and 2% as other.

In 2010, the median age for Indianapolis was 33.7 years. Age distribution for the city's inhabitants was 25% under the age of 18; 4.4% were between 18 and 21; 16.3% were age 21 to 65; and 13.1% were age 65 or older. For every 100 females, there were 93 males. For every 100 females age 18 and over, there were 90 males.

The U.S. Census of 2010 reported 332,199 households in Indianapolis, with an average household size of 2.42 and an average family size of 3.08. Of the total households, 59.3% were family households, with 28.2% of these including the family's own children under the age of 18; 36.5% were husband-wife families; 17.2% had a female householder (with no husband present) and 5.6% had a male householder (with no wife present). The remaining 40.7% were non-family households. As of 2010, 32% of the non-family households included individuals living alone, 8.3% of these households included individuals age 65 years of age or older.

The U.S. Census Bureau's 2007–2011 American Community Survey indicated the median household income for Indianapolis city was $42,704, and the median family income was $53,161. Median income for males working full-time, year-round, was $42,101, compared to $34,788 for females. Per capita income for the city was $24,430, 14.7% of families and 18.9% of the city's total population living below the poverty line (28.3% were under the age of 18 and 9.2% were age 65 or older).

Based on 2015 estimates, the Indianapolis metropolitan area had the 18th highest percentage of LGBT residents in the U.S., with 4.2% of residents identifying as gay, lesbian, bisexual, or transgender.

In 2015, Brookings characterized the Indianapolis metropolitan area as a minor-emerging immigrant gateway with a foreign-born population of 126,767, or 6.4% of the total population, a 131% increase from 2000. Much of this growth can be attributed to thousands of Burmese-Chin refugees that have settled in Indianapolis, particularly Perry Township, since the late-1990s. Indianapolis is home to one of the largest concentrations of Chin people outside of Myanmar (formerly Burma), with an estimated population of 17,000 to 20,000.

Of the 42.42% of the city's residents who identify as religious, Roman Catholics make up the largest group, at 11.31%. The second highest religious group in the city are Baptists at 10.31%, with Methodists following behind at 4.97%. Presbyterians make up 2.13% of the city's religiously affiliated population, followed by Pentecostals and Lutherans. Another 8.57% are affiliated with other Christian faiths. 0.32% of religiously affiliated persons identified themselves as following Eastern religions, while 0.68% of the religiously affiliated population identified as Jewish, and 0.29% as Muslim. According to the nonpartisan and nonprofit Public Religion Research Institute's American Values Atlas, 22% of residents identify as religiously "unaffiliated," consistent with the national average of 22.7%.

Indianapolis is the seat of the Roman Catholic Archdiocese of Indianapolis. Joseph W. Tobin, C.Ss.R., served as archbishop from 2012 to 2017 and was elevated to cardinal in November 2016. On June 13, 2017, Pope Francis announced Charles C. Thompson would replace Tobin, who was reassigned to the Roman Catholic Archdiocese of Newark in January 2017. The archdiocese also operates Bishop Simon Bruté College Seminary, affiliated with Marian University, while the Christian Theological Seminary is affiliated with the Christian Church (Disciples of Christ).

Indianapolis is the seat of the Episcopal Diocese of Indianapolis, based from Christ Church Cathedral. The Indiana-Kentucky Synod of the Evangelical Lutheran Church in America and the Indiana Conference of the United Methodist Church are also based in the city.