A promising approach for addressing a range of diseases lies in the delivery of functional biomacromolecules such as nucleic acids or proteins to cells. Polymers, peptides and the different shapes accessible through self-assembly of polymeric and peptidic amphiphiles have been widely explored as carriers and as containers for reactions on the nanoscale. These building blocks are particularly interesting, because several essential parameters such as physical characteristics, conditions for degradation or biocompatibility can be tuned to suit specific requirements. In this review, different three-dimensional architectures ranging from dendrimers and hyperbranched molecules to micelles, vesicles and nanoparticles assembled from synthetic polymers and peptides are discussed. It is focused on their function as a carrier for biologically active macromolecules, highlighting seminal examples from the current literature and pointing out the remaining and upcoming challenges in this important area of research.