Cyclooxygenase (COX) enzymes, including constitutively expressed COX-1 (mediating basic housekeeping functions) and primarily inducible COX-2 (involved in inflammation, hyperalgesia, cell proliferation, and colorectal cancer), are key targets for nonsteroidal antiinflammatory drugs (NSAIDs). Traditional NSAIDs inhibit both COX-1 (causing ulcerogenic side effects) and COX-2 (providing antiinflammatory and analgesic effects). COX-2 selective inhibitors reduce gastrointestinal toxicity and may prevent colorectal cancer but have raised cardiovascular safety concerns. While there are excellent reviews on COX structure, mechanism, and inhibitor structure-function relationships, this review focuses on the structural and functional basis of COX inhibition by nonselective and COX-2 selective inhibitors. It integrates kinetic, mechanistic, and structural information to illustrate not only the range of molecules with COX inhibitory activity but also the diversity of mechanisms by which they act.