Messenger RNA (mRNA)-based therapies offer great promise for the treatment of a variety of diseases. In 2020, two FDA approvals of mRNA-based vaccines have elevated mRNA vaccines to global recognition. However, the therapeutic capabilities of mRNA extend far beyond vaccines against infectious diseases. They hold potential for cancer vaccines, protein replacement therapies, gene editing therapies, and immunotherapies. For realizing such advanced therapies, it is crucial to develop effective carrier systems. Recent advances in materials science have led to the development of promising nonviral mRNA delivery systems. In comparison to other carriers like lipid nanoparticles, polymer-based delivery systems often receive less attention, despite their unique ability to carefully tune their chemical features to promote mRNA protection, their favorable pharmacokinetics, and their potential for targeting delivery. In this review, the central features of polymer-based systems for mRNA delivery highlighting the molecular design criteria, stability, and biodistribution are discussed. Finally, the role of targeting ligands for the future of RNA therapies is analyzed.