Polymersomes, the structural analogues of liposomes, are hollow structures enclosed by a bilayer membrane made from amphiphilic copolymers. Polymersomes have been proposed to mimic the structure and properties of cellular membranes and viral capsids. Excellent robustness and stability, chemical versatility for tunable membrane properties and surface functionalization make polymersomes attractive candidates for drug delivery, diagnostic imaging, nanoreactor vessels, and artificial organelles. In further biomimetic strategies, stimuli-responsive polymersomes that can recognize various external physical or internal biological environmental stimuli and conduct "on demand" release in dose-, spatial-, and temporal-controlled fashions have been widely developed. This Perspective focuses on recent advances in stimuli-responsive polymersomes and their potential biomedical applications. Representative examples of each stimulus, the advantages and limitations of different strategies, and the future opportunities and challenges are discussed.