Polymersomes, which are stable and robust vesicles made of block copolymer amphiphiles, are good candidates for drug carriers or micro/nanoreactors. Polymer chemistry enables almost unlimited molecular design of responsive polymersomes whose degradation upon environmental changes has been used for the slow release of active species. Here, we propose a strategy to remotely trigger instantaneous polymersome bursting. We have designed asymmetric polymer vesicles, in which only one leaflet is composed of responsive polymers. In particular, this approach has been successfully achieved by using a UV-sensitive liquid-crystalline copolymer. We study experimentally and theoretically this bursting mechanism and show that it results from a spontaneous curvature of the membrane induced by the remote stimulus. The versatility of this mechanism should broaden the range of applications of polymersomes in fields such as drug delivery, cosmetics and material chemistry.