Over the last three decades but more particularly during the last 5 years, auxetic mechanical metamaterials constructed from precisely architected polymer-based materials have attracted considerable attention due to their fascinating mechanical properties. These materials present a negative Poisson's ratio and therefore unusual mechanical behavior, which has resulted in enhanced static modulus, energy adsorption, and shear resistance, as compared with the bulk properties of polymers. Novel advanced polymer processing and fabrication techniques, and in particular additive manufacturing, allow one to design complex and customizable polymer architectures that are particularly relevant to fabricate auxetic mechanical metamaterials. Although these metamaterials exhibit exotic mechanical properties with potential applications in several engineering fields, biomedical applications seem to be one of the most relevant with a growing number of articles published over recent years. As a result, special focus is needed to understand the potential of these structures and foster theoretical and experimental investigations on the potential benefits of the unusual mechanical properties of these materials on the way to high performance biomedical applications. The present Review provides up to date information on the recent progress of polymer-based auxetic mechanical metamaterials mainly fabricated using additive manufacturing methods with a special focus toward biomedical applications including tissue engineering as well as medical devices including stents and sensors.