The 1 train is generally the Subway’s and Manhattan’s westernmost subway line (especially if you remove the fact that Manhattan is at a 29-degree angle to the Northeast, not at true north, which means that Bay Ridge is technically farther west than Upper and most of Manhattan). The exceptions are between 207 Street and 168 Street, where the A is west of it, and between 59 Street and just south of 14 Street (the lines cross without an interchange station) where the 8th Avenue subway (A,C,E) is one block west. The L and 7 train also cross the 1 train on their crosstown journeys across 14 Street and from 42 Street to 34 Street-Hudson Yards. The 1 train was the undisputed westernmost subway line, from the lines completion between South Ferry and 242 Street with the completion of the 7 Avenue Subway at 34 Street in 1918 until the 8th Avenue Subway (IND) opened in 1932 with no subway lines west of it.
The northern portion of the line between 42 Street and 145 Street was part of the Opening Day on the IRT, opening on October 27, 1904. It was extended in a few phases (hardest extension to build was through the Washington Heights and Fort George deep-level tunnels) to reach 242 Street-Van Cortlandt Park in 1908. The southern portion of the line opened in 1917 (as a Shuttle from Times Square to Penn Station) and onto South Ferry in 1918, creating the IRT "H" system including the current routings we have today.
The 1 train, except during late nights when 2 trains also run local, is one of just 4 subway lines (not including 2 of the shuttles) that never share its tracks with any other line (others are 6,7 and L trains). This means service is extremely frequent with trains up to every 3 minutes during the peak of rush hour, every 6 minutes during middle of the day and evenings on Weekdays. Weekend service is every 8 minutes.
The line is majority underground, except for the 125 Street station which is located on a viaduct due to the topography of the Manhattanville, and from Dyckman Street north to 242 Street (including crossing over the Broadway Bridge over the Manhattan Ship Canal, part of the diverted Harlem River). The topography of northern Manhattan was again taken advantaged of at Dyckman Street where trains don’t go up and down before becoming elevated but simply stay at the same elevation coming out of the steep Fort George Hill after stopping at the previous stop 191 Street, the deepest subway station at 173 feet below street level.
The majority of the line has more than 2 tracks with 4 tracks between Chambers and 96 Street, where 2 and 3 trains run express, and 3 tracks north of 96 Street until between 145 and 157 Street where the line becomes 2 tracks through the Deep-bore tunnel through Washington Heights, with 3 tracks resuming north of Dyckman Street before ending just before the two-track 242 Street terminal. After the express tracks leave to go to Brooklyn south of Chambers Street, the last mile to South Ferry is also just a two-tracks subway.
From August 21, 1989 through May 27, 2005 (with a one-year break from September 11, 2001 through September 15, 2002 after the Courtlandt Street station was distroyed, temporarily rerouting 1 trains via the 3 line to New Lots Avenue in Brooklyn) the 1 train operated skip-stops in Upper Manhattan, with 1 trains skipping 4 stops: 145 Street, 191 Street, 207 Street, and 225 Street in Upper Manhattan. The 9 train operated as the 1 trains counterpart, serving the stops skipped by the 1 train, while skipping 157 Street, Dyckman Street, 215 Street and 238 Street. This service pattern originally operated in both directions during both rush hours and middays, before being reduced to rush hours only in 1994 (at the same time 191 Street was changed to an all stop from a skip-stop).
The 9 train was created and skip-stop service was done to allow all Broadway Local trains to be extended north of 137 Street (in 1989 every other 1 train terminated during rush hours at 137 Stret) to 242 Street, and the faster travel times created by the skip-stop service patterns were needed, because at the time there weren't enough train cars to simply double service north of 137 Street with all trains running local.
For Rolling stock, the 1 train runs exclusively R62A trains, it and the 3 train are the two IRT lines to have never had R142 or R142A “New Technology Trains” assigned to run on it.