Engineered polymer vesicles, termed as polymersomes, confer a flexibility to control their structure, properties, and functionality. Self-assembly of amphiphilic copolymers leads to vesicles consisting of a hydrophobic bilayer membrane and hydrophilic core, each of which is loaded with a wide array of small and large molecules of interests. As such, polymersomes are increasingly being studied as carriers of imaging probes and therapeutic drugs. Effective delivery of polymersomes necessitates careful design of polymersomes. Therefore, this review article discusses the design strategies of polymersomes developed for enhanced transport and efficacy of imaging probes and therapeutic drugs. In particular, the article focuses on overviewing technologies to regulate the size, structure, shape, surface activity, and stimuli- responsiveness of polymersomes and discussing the extent to which these properties and structure of polymersomes influence the efficacy of cargo molecules. Taken together with future considerations, this article will serve to improve the controllability of polymersome functions and accelerate the use of polymersomes in biomedical applications.