Compartmentalization is a fundamental principle in biology that is needed for the temporal and spatial separation of chemically incompatible reactions and biomolecules. Nano- or micro-sized compartments made of synthetic polymers are used to mimick this principle. The self-assembly of these polymers into vesicular objects is highly compatible with the integration of biomolecules, either into the lumen, the membrane or onto the surface of the vesicles. Thus, a great variety of biohybrid nano- and microscaled compartments has been developed exploiting the specific function and properties of targeting peptides, antibodies, enzymes, nucleic acids or lipids. Such biohybrid compartments have moved from simple systems encapsulating e.g. a model protein into complex multicompartmentalized structures that are able to combine the activity of different biomolecular cargos getting closer to the realization of artifical organelles or cells. Encapsulation of medically relevant cargos combined with careful design of the polymeric scaffold and specific surface functionalization have led to a significant progress in therapeutical applications such as targeted drug delivery or enzyme replacement therapy.