This review article gathers the most recent recycling technologies for thermoset and thermoplastic polymers. Results about existing experimental procedures and their effectiveness are presented. For thermoset polymers, the review focuses mainly on fibre-reinforced polymer composites, with an emphasis on epoxy-based systems and carbon/glass fibres as reinforcement, due to the environmental concerns of their end-of-life management. Thermal processes (fluidised bed, pyrolysis) and chemical processes (different types of solvolysis) are discussed. The most recent combined processes (microwave, steam, and ultrasonic assisted techniques) and extraordinary recycling attempts (electrochemical, biological, and with ionic liquids) are analysed. Mechanical recycling that leads to the downgrading of materials is excluded. Insights are also given for the upcycling methodologies that have been implemented until now for the reuse of fibres. As for thermoplastic polymers, the most state-of-the-art recycling approach for the most common polymer matrices is presented, together with the appropriate additivation for matrix upcycling. Mechanical, chemical, and enzymatic recycling processes are described, among others. The use of fibre-reinforced thermoplastic composites is quite new, and thus, the most recent achievements are presented. With all of the above information, this extensive review can serve as a guide for educational purposes, targeting students and technicians in polymers recycling.