Single-stranded messenger ribonucleic acid (mRNA) plays a pivotal role in transferring genetic information, and tremendous effort has been devoted over the years to utilize its transcription efficacy in therapeutic interventions for a variety of diseases with high morbidity and mortality. Lipid nanocarriers have been extensively investigated for mRNA delivery and enabled the rapid and successful development of mRNA vaccines against SARS-CoV-2. Some constraints of lipid nanocarriers have encouraged the development of alternative delivery systems, such as polymer-based soft nanoparticles, which offer a modular gene delivery platform. Such macromolecule-based nanocarriers can be synthetically articulated for tailored parameters including mRNA protection, loading efficacy, and targeted release. In this review, we highlight recent advances in the development of polymeric architectures for mRNA delivery, their limitations, and the challenges that still exist, with the aim of expediting further research and the clinical translation of such formulations.