Gemini 10 was designed to achieve rendezvous and docking with an Agena Target Vehicle (ATV), and EVA. It was also planned to dock with the ATV from the Gemini 8 mission. This Agena's battery power had failed months earlier, and an approach and docking would demonstrate the ability to rendezvous with a passive object. It would be also the first mission to fire the Agena's own rocket, allowing them to reach higher orbits.

Gemini 10 established that radiation at high altitude was not a problem. After docking with their Agena booster in low orbit, Young and Collins used it to climb temporarily to 412.4 nautical miles (763.8 km). After leaving the first Agena, they then rendezvoused with the derelict Agena left over from the aborted Gemini 8 flight—thus executing the program's first double rendezvous. With no electricity on board the second Agena, the rendezvous was accomplished with eyes only—no radar.

After the rendezvous, Collins spacewalked over to the dormant Agena at the end of a 50-foot (15 m) tether, making him the first person to meet another spacecraft in orbit. Collins then retrieved a cosmic dust-collecting panel from the side of the Agena. As he was concentrating on keeping his tether clear of the Gemini and Agena, Collins' Hasselblad camera worked itself free and drifted away, so he was unable to take photographs during the spacewalk.