Apollo-Soyuz Test Project

 Apollo Crew: Deke Slayton (Docking Module Pilot)
                  Tom Stafford (Commander)
                   Vance Brand (Command Module Pilot)

Backup Apollo Crew: Al Bean (Commander)
                            Ron Evans (Command Module Pilot)
                            Jack Lousma (Docking Module Pilot)

Apollo Mission: July 15 - 24, 1975

Soyuz Crew: Alexei Leonov (Commander)
                 Valeri Kubasov (Flight Engineer)

Soyuz Backup Crew: Anatoli Filipchenko (Commander)
                           Nikolai Rukavishnikov (Flight Engineer)

Soyuz Mission: July 15 - 21, 1975

Throughout the 1950's and 60's there has been a space race and the cold war in between Russia and the US.  When the ASTP happened, Tom Stafford and Alexei Leonov shook hands in orbit, it ended.