The names IRT, BMT, and IND were the names of the three competing transit agencies prior to city takeover in the 1940.

The Interborough Rapid Transit (IRT) Company was a private organization managed by financier August Belmont. The arrangement with the city, known now as "Contract One" was such that ownership of the line would be retained by the city, with construction and operational responsibility granted to the IRT Company. Construction on this first subway began in 1900, and service started on October 27, 1904. Its route followed today's #4-5-6 line from City Hall to 42nd Street, turning west into today's shuttle line with stops at Grand Central and Times (Longacre) Square, then turning north following today's #1-2-3 lines to 145th Street and Broadway. A Bronx route was constructed simultaneously and connected initially to the 3rd Avenue El, and then to the subway in 1905. The line was soon extended ("Contract Two") to Atlantic Ave, Brooklyn, in 1908. The IRT also leased the Manhattan Railway elevated lines, the 2nd, 3rd, 6th, and 9th Avenue Elevated lines in Manhattan and the Bronx, for 999 years, as part of their operational contract with the city.

The Brooklyn-Manhattan Transit (BMT, formerly the Brooklyn Rapid Transit, BRT) was the rapid transit company which built, bought, or assumed control of the Brooklyn elevated lines (the Culver, West End, Lexington, Myrtle, Broadway, Fulton, and Fifth Avenue Els, of which the Culver, West End, Broadway and parts of the Fulton and Myrtle still exist), and the ground-level extensions to southern Brooklyn, of which the Sea Beach and Brighton Beach were rebuilt for subway service.

Beginning in 1913, the city embarked on a project called the "Dual Contracts", under which the city built additional lines that were operated as part of the IRT and BMT systems. Finished mostly by 1920, some of the new lines (the Flushing and the Astoria lines in Queens) had trains operated by both companies. The Dual Contracts IRT lines were the Seventh Ave (south from Times Square) and Lexington Ave (north from Grand Central); the Jerome, White Plains Road and Pelham Bay Park branches in the Bronx, and the Brooklyn lines beyond Atlantic Ave. The BMT lines were the Broadway Subway and Nassau Street Subway in Manhattan, the 14th St.-Eastern District line from Manhattan to Brooklyn, and Fourth Ave., West End, and Culver lines in Brooklyn. Connections were also made to the company's Sea Beach and Brighton Beach lines.

The Independent Subway (IND) was formed by the City in the 1920s as a subway that would be "independent" of manipulation by the IRT and BMT companies. Initially a private operator was sought but eventually, the City's Board of Transportation began operation itself. This system consisted of entirely subway construction with only one elevated portion, a short section over the Gowanus Canal in Brooklyn. The IND lines were the 8th Avenue and 6th Avenue trunk lines in Manhattan, the Queens Boulevard subway in Queens, the Concourse subway in the Bronx, the Fulton Street subway in Brooklyn, the Brooklyn/Queens Crosstown, and the line in Brooklyn via Smith/9th Sts. to Church Avenue. Certain IND lines underpinned existing IRT and BMT elevated lines with the intention of eventually replacing them.

The trains of the BMT and IND lines are longer and wider than those of the IRT lines. Therefore an BMT/IND style train cannot fit into an IRT tunnel. An IRT train CAN fit into a BMT/IND tunnel but since it is narrower the distance from car to platform is unsafe. Cars from the IRT division are moved using BMT/IND tracks to Coney Island Overhaul Shops for major maintenance on a regular basis.

After city takeover of the bankrupt BMT and IRT companies on June 1, 1940, many of the elevated lines were closed, and a slow "unification" took place, marked notably by establishment of several free transfer points between divisions in 1948 and a few points of through running between IND and BMT lines beginning in 1954. The Chrystie Street connection in Manhattan, which opened in November 1967, unified the Manhattan Bridge lines of the BMT with the Sixth Avenue lines of the IND, such that trains from Brooklyn now had access to all of the BMT and IND trunk lines in Manhattan (6th, 8th, Broadway, and Nassau St.). The 63rd Street Tunnel connection forms another link between the Broadway BMT Subway and Sixth Avenue IND Subway and the Queens Boulevard IND Subway.

Officially, the names IRT, BMT, and IND are no longer used. Beginning in 1967, the former systems were designated as the "A Division" (ex-IRT lines), "B-1 Division" (BMT lines), and "B-2 Division" (IND lines). The distinction between the B divisions is blurred because of the unification projects noted above.

Which current lines were part of which old system?

• 1,2,3,4,5,6,7,9, Grand Central Shuttle: IRT
• A: IND from 207th Street to the tunnel portal between Grant Avenue and 80th Street/Hudson Street. Elevated section from 80th Street/Hudson Street to Lefferts Blvd. former BMT Fulton Street elevated line. This portion of the Fulton el was connected to the IND in 1956. The whole Rockaway line, which branches at Rockaway Blvd was built by the Long Island Rail Road, and became a subway line in 1956.
• B: IND from 205th Street to Broadway-Lafayette. BMT from the Manhattan Bridge to Coney Island. The Chrystie Street connector (which includes Grand Street station) built by the MTA after unification opened in 1967 connecting the two portions. The B runs part of the day to 21st Street-Queensbridge, built after unification and not part of either the former IND or BMT.
• C: IND from 168th Street to Euclid Ave.
• D: IND from 205th Street to Broadway-Lafayette. BMT from the Manhattan Bridge to Coney Island. The Chrystie Street connector (which includes Grand Street station) built by the MTA after unification opened in 1967 connecting the two portions.
• E: IND from Van Wyck Blvd. to World Trade Center. The section between Jamaica/Van Wyck and Parsons/Archer was built after unification and opened in 1988.
• F: IND from 179th to Church Ave. tunnel portal. BMT from Ditmas Ave. to Coney Island. The BMT portion of the route, known as the "Culver Line", was connected to the IND line in 1954. The Culver Line formerly connected to the West End line at 9th Ave. via a no-longer-existing elevated structure. The Ditmas Avenue-9th Avenue section operated as the "Culver Shuttle" until its abandonment in 1975.
• G: IND along entire length.
• J/Z: BMT from 121st St. to Broad Street. The section between 121st St and Parsons/Archer was built after unification and opened in 1988.
• L: BMT along entire length.
• M: BMT along entire length.
• N: BMT along entire length. The line between Queensboro Plaza and Astoria, and the portion of the #7 between Queensboro Plaza and Main St. Flushing were jointly operated by the BMT and the IRT until 1948.
• Q: IND from 47th-50th Streets to Broadway-Lafayette. BMT from Manhattan Bridge to Brighton Beach. The Chrystie Street connector (which includes Grand Street station) built by the MTA after unification opened in 1967 connecting the two portions. The section north of 47-50th St. to 57th St. opened in 1968, after the divisons were eliminated, but can be certainly considered IND. The section between 57th St. and 21st St-Queensbridge was opened in 1989.
• R: BMT from 60th Street Tunnel to 95th Street. The "11th Street Connector", which connects the BMT tunnel to the IND Queens Boulevard line, opened in 1955 and was the second of the inter-divisional connections to open.
• S (Franklin Shuttle): BMT along entire length.