Cook Islands is one of the dependent territories of New Zealand and is the only one that has ever participated in the Summer Olympics. They first showed up in 1988 in Seoul, South Korea when they sent their biggest delegations to date.
Runners William Taramai and Erin Tierney, boxers Zekaria Williams, Richard Pittman and Terepai Maea, and weightlifters Joseph Kavuai and Michael Tererui made up Cook Islands' first-ever delegation to the Summer Games. Of the seven, only the weightlifters were able to finish their events. Kavuai ranked 25th and Tererui managed a 16th place finish.
As a matter of fact, since their first appearance in the 1988 Summer Games, most of the athletes that were able to finish their events were weightlifters. Cook Islands is yet to produce their first Olympic medalist. Luisa Peters is Cook Islands' best Olympian so far managing a 12th place finish in the 2012 Summer Games in London, England. The next best event for Cook Islands is sailing which is not that hard to believe since the territory is made up of relatively small islands.
As with most of territories of its size and type, Cook Islands has never sent a delegation to any Winter Olympic meets.