Polymeric materials have been accumulating in the environment for decades as a result of the linear way of consuming plastics. Unfortunately, the current approaches followed to treat such a large amount of plastic waste, mainly involving physical recycling or pyrolysis, are not efficient enough. Recently, chemical degradation has emerged as a long-term strategy towards reaching completely sustainable cycles where plastics are polymerised, depolymerised, and then re-polymerised with minimal changes in their quantity or final properties. Organocatalysts, which are promising “green” substitutes for traditional organometallic complexes, are able to catalyse depolymerisation reactions yielding highly pure small molecules that are adequate for subsequent polymerisations or other uses. Moreover, by varying several reaction parameters (e.g. solvent, temperature, concentration, co-catalyst, etc.), the depolymerisation products can be tuned in innumerable possibilities, which further evidences the versatility of depolymerisation. In this review, we highlight the recent advances made by applying organocatalysts, such as organic bases, organic acids, and ionic compounds, to chemically degrade the most commonly used commercial polymers. Indeed, organocatalysis is envisaged as a promising tool to reach a circular and environmentally friendly plastic economy.