A rescue mission or rescue operation was a movement with the goal to save someone from a situation or another party. They were carried out by rescue teams.

While under the influence of trellium, T'Pol threatened to kill Jonathan Archer, believing the mission was to eliminate the Vulcan crewmembers aboard the Seleya. Archer tried to explain her that they are on a rescue mission and pointed to the stun setting of their phase-pistols. (ENT: "Impulse")

In 2372, Tom Paris was charged with leading a rescue mission to bring back Kathryn Janeway, B'Elanna Torres, and Tuvok from a Mokra Order prison. (VOY: "Resistance")

In 2375, the crew of the Voyager started a rescue mission for Tuvok, Tom Paris, The Doctor, and Noss who were trapped in a subspace sinkhole. (VOY: "Gravity")