Protein-polymer conjugates are a class of molecules that combine the stability of polymers with the diversity, specificity, and functionality of biomolecules. These bioconjugates can result in hybrid materials that display properties not found in their individual components and can be particularly relevant for drug delivery applications. Engineering amphiphilicity into these bioconjugate materials can lead to phase separation and the assembly of high-order structures. The assembly, termed self-assembly, of these hierarchical structures entails multiple levels of organization: at each level, new properties emerge, which are, in turn, influenced by lower levels. Here, we provide a critical review of protein-polymer conjugate self-assembly and how these materials can be used for therapeutic applications and drug delivery. In addition, we discuss central bioconjugate design questions and propose future perspectives for the field of protein-polymer conjugate self-assembly.