Challenges in establishing a circular economy of carbon-fiber-reinforced plastics (CFRP) arise in particular from the necessary but problematic separation of the fiber from the matrix. The pyrolysis process is a possible technology for composite separation that has already been industrially implemented. A further development is microwave-assisted pyrolysis, in which the CFRP material is heated by the microwaves to expose the fiber. Process fundamentals and influences on fiber-matrix separation are considered in this article.