Organocatalysis has become an invaluable tool for polymer synthesis, and its utility has been demonstrated in ring-opening, anionic, zwitterionic, and group-transfer polymerizations. Despite this, the use of organocatalysis in other polymerization reactions such as step-growth polymerizations remains underexplored, relative to more traditional metal-based polymerizations. Recently, the use of organic bases such as guanidines, amidines, N-heterocyclic carbenes, and organic "strong or super-strong" Brønsted acids to catalyze the synthesis of metal-free polyurethanes has shown to be competitive to commercially widely used dibutyltin dilaurate and dibutyltin diacetate catalysts. This Perspective article highlights recent advances in organocatalyst design for isocyanate-based polyurethane synthesis with the aim of comparing the activity and selectivity of each of the new catalytic reactions to each other and the traditional metal-based catalysts. The article also draws attention to new trends in isocyanate-free polyurethane synthesis and the key role that organocatalysis is playing in these innovative polymerization processes.