Perfect modals are used to talk about unfulfilled obligations or possibilities in the past. They include could have, may/might have, must have, should have/shouldn't have, and can't have. Each modal has a specific use - could have expresses ability or opportunity, may/might have expresses weak possibility, must have expresses logical conclusion, should have/shouldn't have expresses regret or obligation, and can't have expresses impossibility. The document provides examples of sentences using each perfect modal.