A treaty is basically an agreement between/among nations over a certain topic or concern. The United States as a sovereign power has been entering into treaties since its inception. This 13-volume series contains the texts of all treaties up to and including 1949. Beginning in 1950, United States Treaties and Other International Agreements presents the full text of agreements on an annual basis. through 1983/84. Individual treaty texts from 1996 to the present are also online. (Yes, the full texts of treaties from 1985 to 1995 are not freely available as far as we can surmise. Something is very wrong with this.)
To find out what treaties are still in effect, please consult the annual Treaties in Force; for post-2013 compilations please go to this State Department site for information. For information on how the U.S. Senate is involved in approving treaties, please come here.