The transition towards safer and more sustainable production of polymers has led to a growing body of academic research into non-isocyanate polyurethanes (NIPUs) as potential replacements for conventional, isocyanate-based polyurethane materials. This perspective article focuses on the opportunities and current limitations of NIPUs produced by the reaction between biobased cyclic carbonates with amines, which offers an interesting pathway to renewable NIPUs. While it was initially thought that due to the similarities in the chemical structure, NIPUs could be used to directly replace conventional polyurethanes (PU), this has proven to be more challenging to achieve in practice. As a result, and in spite of the vast amount of academic research into this topic, the market size of NIPUs remains negligible. In this perspective, we will emphasize the main limitations of NIPUs in comparison to conventional PUs and the most significant advances made by others and us to overcome these limitations. Finally, we provide our personal view of where research should be directed to promote the transition from the academic to the industrial sector.