The Apollo mission was officially not numbered, though some sources refer to it as "Apollo 18".
The Apollo-Soyuz Test Project (ASTP) took place in the second half of July 1975 and entailed the docking of an American Apollo spacecraft with the Soviet Soyuz 19 spacecraft. Whilst the Soyuz was given a mission designation number as part of the ongoing Soyuz program, it was referred to simply as "Soyuz" through the duration of the joint mission. On the Soviet side, the Soyuz flew with two men: Alexey Leonov and Valery Kubasov. Leonov was the first man to walk in space in 1965 on Voskhod 2, and Kubasov had flown on Soyuz 6 in 1969. Both were slated to have flown on the ill-fated Soyuz 11 in 1971 (Leonov as commander, Kubasov as the flight engineer), but were grounded because Kubasov was suspected to have tuberculosis. The Apollo flew with a three-man crew onboard: Tom Stafford, Vance Brand and Deke Slayton. Slayton was one of the original Mercury 7 astronauts selected in 1958 but had been grounded due to a heart problem. Slayton became head of NASA's astronaut office and after a lengthy medical program, selected himself for this mission. At the time, it made him both the oldest person to fly in space and the longest gap between selection as an astronaut and flight into space. Vance Brand had trained with the Apollo Spacecraft used for this mission during his time as a backup Apollo 15 command module pilot as well as multiple stints as a backup Skylab commander.
The Soyuz and Apollo flights launched within seven and a half hours of each other on July 15, and docked on July 17. Three hours later the two mission commanders, Stafford and Leonov, exchanged the first international handshake in space through the open hatch of the Soyuz. NASA had calculated that the historic handshake would have taken place over the British seaside resort of Bognor Regis, but a delay resulted in its actual occurrence being over the town of Metz in France.
The two spacecraft remained linked for 44 hours, long enough for the three Americans and two Soviets to exchange flags and gifts (including tree seeds which were later planted in the two countries), sign certificates, pay visits to each other's ships, eat together and converse in each other's languages. (Because of Stafford's pronounced drawl when speaking Russian, Leonov later joked that there were actually three languages spoken on the mission: Russian, English, and "Oklahomski.") There were also docking and redocking maneuvers during which the two spacecraft reversed roles and the Soyuz became the "active" ship. The Soviets remained in space for five days, the Americans for nine, during which the Apollo crew also conducted experiments in Earth observation.
Soyuz spacecraft as seen from Apollo CM While docked, the two crews conducted joint scientific experiments and spent time in each others' craft. After forty-four hours together, the two ships separated, and maneuvered to use the Apollo to create an artificial solar eclipse to allow the crew of the Soyuz to take photographs of the solar corona. Another brief docking was made before the ships went their separate ways.
The mission was a great success, both technically and as a public-relations exercise for both sides.
A minor planet, 2228 Soyuz-Apollo, discovered in 1977 by Soviet astronomer Nikolai Stepanovich Chernykh, is named after the mission.