The Second Avenue Subway, a New York City Subway line that runs under Second Avenue on the East Side of Manhattan, has been proposed since 1920; the first phase of the line did not open until 2017. Up until the 1960s, many distinct plans for the Second Avenue subway line were never carried out, though small segments were built in the 1970s. The complex reasons for these delays are why the line has been called "the line that time forgot".

The line was originally proposed in 1920 as part of a massive expansion of what would become the Independent Subway System (IND). The Great Depression crushed the original proposal, and lack of funds scuttled numerous revivals throughout the 20th century. Meanwhile, the elevated lines along Second Avenue and Third Avenue, which the Second Avenue Line was intended to replace, were respectively demolished in 1942 and 1955, leaving the Lexington Avenue Subway as the only rapid transit line on much of Manhattan's east side.

Construction of tunnels began in 1972 as part of the Program for Action, but was halted in 1975 because of the city's fiscal crisis, with only a few short segments of tunnel having been completed. Meanwhile, construction of the 63rd Street Lines, which would connect the Second Avenue Line and the IND Queens Boulevard Line to the BMT Broadway Line and the IND Sixth Avenue Line, began in 1969. The first segment of the 63rd Street Lines, which opened on October 29, 1989, included provisions for future connections to the Second Avenue Line. When the construction of the Second Avenue Subway finally commenced in the 21st century, the Lexington Avenue Line was by far the busiest subway line in the United States, with an estimated 1.3 million daily riders in 2015. The first phase of the Second Avenue Subway opened in 2017, and a second phase is under development as of 2024^[update].

After World War I, the New York City Subway experienced a surge in ridership. By 1920, 1.3 billion annual passengers were riding the subway, compared to 523 million annual riders just seven years before the war. The same year, the New York Public Service Commission launched a study at the behest of engineer Daniel L. Turner to determine what improvements were needed in the city's public transport system. Turner's final paper, titled Proposed Comprehensive Rapid Transit System, was a massive plan calling for new routes under almost every north-south Manhattan avenue, extensions to lines in Brooklyn and Queens, and several crossings of the Narrows to Staten Island. Massively scaled-down versions of some of Turner's plans were found in proposals for the new city-owned Independent Subway System (IND). Among the plans was a massive trunk line under Second Avenue consisting of at least six tracks and numerous branches throughout Brooklyn, Queens, and the Bronx. Turner also proposed that the two elevated lines be knocked down to make room for the 6-track Second Avenue Subway. The plan was to connect the new line to the then-unbuilt Sixth Avenue and Eighth Avenue subway lines. A proposal for a Third Avenue subway was also put forth, as was another one for a First Avenue Subway. However, in the initial version of the plan, an East Side subway was not prioritized as part of the IND's construction, regardless of whether it was under First, Second, or Third Avenues.

In January 1927, Turner submitted a revised proposal. It was now going to connect to a Tenth Avenue trunk line as well as to crosstown lines in the Bronx and Queens. The Second Avenue Subway was still a six-track line through Manhattan, except for a short eight-track tunnel at its junction with the Queens lines. The plan called for a connection to the IND Concourse Line in the Bronx, as well as another one to the IND Fulton Street Line in Brooklyn. Such a plan would have cost $165,000,000 (equivalent to $2,987,000,000 in 2024), including connections and underwater crossings. As the IRT Lexington Avenue Line got more crowded, some suggested ideas that were considered unusual. One suggestion included a new tunnel under Lexington Avenue, while another included a tunnel under a separate right-of-way between Second and Third Avenue.

On September 16, 1929, the Board of Transportation of the City of New York (BOT) tentatively approved the expansion, which included a Second Avenue Line with a projected construction cost of $98,900,000 (equivalent to $1,795,000,000 in 2024), not counting land acquisition. From north to south, the 1929 plan included four tracks from the Harlem River (where it would continue north as a Bronx trunk line with several branches) to 125th Street, six tracks from 125th Street to a link with the Sixth Avenue Line at 61st Street, four tracks from 61st Street to Chambers Street, and two tracks from Chambers Street to Pine Street. The plan was soon modified with the addition of another Bronx branch, as well as an extension of the subway to Water and Wall Streets. At the time, it was supposed to be completed between 1938 and 1941. In anticipation of the line's opening, real estate prices along the proposed route rose by an average of 50%. There were high demand for tenements along the route of the proposed subway, and sites located at street corners along the route were quickly bought up.

Due to the Great Depression, the soaring costs of the expansion became unmanageable. Construction on the first phase of the IND was already behind schedule, and the city and state were no longer able to provide funding. By 1930, the line was shortened to between 125th and 34th Streets, with a turnoff at 34th Street and a crosstown connection there; this line was to be complete by 1948. The line above 32nd Street was to start construction in 1931, with construction of a southern extension to Houston Street to commence in 1935; these segments would open in 1937 and 1940, respectively. By 1932, the Board of Transportation had modified the plan to further reduce costs, omitting a branch in the Bronx, and truncating the line's southern terminus to the Nassau Street Loop.

Further revision of the plan and more studies followed. By 1939, construction had been postponed indefinitely, and the Second Avenue Line was relegated to "proposed" status. The Board of Transportation had ranked it as the city's 14th most important transportation project. The Second Avenue Line was also cut to two tracks, but now had a connection to the BMT Broadway Line. The reduced plan now had a single northern branch through Throggs Neck, Bronx, and a branch south into Brooklyn, connecting to a stub of the IND Fulton Street Line at the Court Street station, which is now the site of the New York Transit Museum. The subway's projected cost went up to US$249 million (equivalent to $5,323,000,000 in 2024). The United States' entry into World War II in 1941 halted all but the most urgent public works projects, delaying the Second Avenue Line once again.