The rapid rise in the applications of carbon fibre reinforced polymer matrix composites (CFRPs) is creating a waste recycling challenge. The use of high-performance thermoset polymers as the matrix makes the recovery of the fibres and the resins extremely difficult. Implementation of a circular economy that can eliminate waste and re-use resources warrants the use of efficient processes to recycle end-of-life CFRP components and manufacturing wastes. To this end, herein we present a critical review of the current technologies for recovering carbon fibres and/or the polymers and re-manufacturing CFRPs. New research opportunities in developing new biodegradable thermosets and thermoplastic matrices are also outlined together with more radical recycling strategies for the future.