Hybrid vesicles resulting from the combined self-assembly of both amphiphilic copolymers and lipids have attracted particular interest from chemists and (bio)physicists over the last five years. Such assemblies may be viewed as an advanced vesicular structure compared to their liposome and polymersome forerunners as the best characteristics from the two different systems can be integrated in a new, single vesicle. To afford such a design, the different parameters controlling both self-assembly and membrane structure must be tuned. This highlight aims to present a comprehensive overview of the fundamental aspects related to these structures, and discuss emerging developments and future applications in this field of research.