The C Train is one of only three lines of the New York City subway whose route is entirely on trackage built by the
Independent subway system (the others being the
E and
G). It is underground along its entire route (a feat it shares only with the
E Train and the
R) and is a local service companion to the
A express along its entirety.
The trackage where the C train runs (The Central Park West and the Eighth Avenue Line in Manhattan, and the Fulton Line in Brooklyn), was built as part of the initial Independent subway in the late 20s and early 30s. The farthest outlying section in Brooklyn, such as the Euclid avenue stop, was part of the last section of the Independent build before the war and as such it has very Art Deco station architecture.
The first service to resemble the current C was the AA local along this same route. Before the MTA went to all single letters in 1986, the C was called the CC.
The C Train currently runs almost exclusively R32 rolling stock, rather ugly cars from the mid 60s. It is also the current home of the R110B test train.