Polyurethane foams (PUFs) are a significant group of polymeric foam materials. Thanks to their outstanding mechanical, chemical, and physical properties, they are implemented successfully in a wide range of applications. Conventionally, PUFs are obtained in polyaddition reactions between polyols, diisoycyanate, and water to get a CO2 foaming agent. The toxicity of isocyanate has attracted considerable attention from both scientists and industry professionals to explore cleaner synthesis routes for polyurethanes excluding the use of isocyanate. The polyaddition of cyclic carbonates (CCs) and polyfunctional amines in the presence of an external blowing agent or by self-blowing appears to be the most promising route to substitute the conventional PUFs process and to produce isocyanate-free polyurethane foams (NIPUFs). Especially for polyhydroxyurethane foams (PHUFs), the use of a blowing agent is essential to regenerate the gas responsible for the creation of the cells that are the basis of the foam. In this review, we report on the use of different blowing agents, such as Poly(methylhydrogensiloxane) (PHMS) and liquid fluorohydrocarbons for the preparation of NIPUFs. Furthermore, the preparation of NIPUFs using the self-blowing technique to produce gas without external blowing agents is assessed. Finally, various biologically derived NIPUFs are presented, including self-blown NIPUFs and NIPUFs with an external blowing agent.