Polymer vesicles, commonly called polymersomes, are spherical shell structures in which an aqueous compartment is enclosed by a bilayer membrane made from amphiphilic block copolymers. Compared to liposomes, their low molecular weight analogues, polymersomes have many superior properties (higher toughness, better stability, tailorable membrane properties), which make them attractive candidates for applications including drug delivery, diagnosis, nanoreactors and templates for micro-or nano-structured materials. Many potential applications require the ability to control the release of substances encapsulated in the interior compartment and /or in the hydrophobic core of membrane. To address this goal, polymersomes have been developed in which a specific stimulus destabilises the vesicular structure. The responsiveness is mainly achieved via proper hydrophobic block design. In this chapter we review the most promising approaches to make stimuli-responsive polymersomes that permit the controlled release of encapsulated contents. Chemical stimuli including hydrolysis, oxidation, reduction and pH change, and physical stimuli including temperature, light, magnetic field, electric field, osmotic shock and ultrasonic wave are discussed, on emphasizing their effects on the chemical and physical structure of the amphiphilic copolymers.