The R&T's current clubhouse was designed by William Symmes Richardson, a partner at McKim, Mead, and White.

[3][4] In addition to offering its members more spacious amenities, the move to Park Avenue afforded more consistent natural light for the skylit playing courts, as well a generally more desirable location.

Board of Directors at this time included financier Ogden Mills and sportsman Harry Payne Whitney.

The structure is representative of the ornate private clubs constructed in New York City during the early 20th century.

Squash National Champions include Palmer Dixon, Lawrence Pool, Beekman Pool, Stephen Vehslage, Peter Briggs, Ralph Howe, John Reese, Jonathan Foster, Morris Clothier, Addison West, Whitten Morris, Michael Ferreira, Dylan Patterson, William Hartigan and Kyle Martino.

Club members who have been elected into the Squash Hall of Fame include William "Treddy" Ketcham, Ralph Howe and Peter Briggs.

The first collegiate squash team match was played at the Racquet and Tennis Club on February 17, 1923.

Amateur Court Tennis Championships include James Van Alen, Ogden Phipps, Alastair Martin, Gene Scott and Morris Clothier.

[8] Tim Chisholm, Head Professional from 1999 to 2004, was World Court Tennis Doubles Champion in 2001 (with Julian Snow).