"Underwatergate" is a great name!

There's a great NY Times best selling book called "Blind Man's Bluff: The Untold Story of American Submarine Espionage" (Hardcover) by Sherry Sontag, Christopher Drew, Annette Lawrence Drewt (1999) that sheds some light on this practice. There are specially built US Navy submarines that exclusivly perform these tasks.

Excerpt from a book review:

"Most of the stories in Blind Man's Bluff have never been told publicly," they write, "and none have ever been told in this level of detail." Among their revelations is the most complete accounting to date of the 1968 disappearance of the U.S.S. Scorpion; the story of how the Navy located a live hydrogen bomb lost by the Air Force; and a plot by the CIA and Howard Hughes to steal a Soviet sub. The most interesting chapter reveals how an American sub secretly tapped Soviet communications cables beneath the waves. Blind Man's Bluff is a compelling book about the courage, ingenuity and America's underwater spies.