Composite materials, especially carbon fiber-reinforced polymers (CFRPs), are high-performance class of structural materials now commonly used in aircraft, marine, and other applications, with emerging large-scale use in the automotive and civil engineering applications. The difficulty of recycling these materials is a key obstacle preventing their further application in larger markets. For decades, the engineering community has pursued physical methods to recover value from end-of-life composite waste. This work has generated scalable methods to recover modest value from CFRP waste, but because of their low value recovery, these are applied to a small fraction of CFRP waste. By contrast, relatively few methods to recycle CFRPs have been based on strategic approaches systematically to deconstruct the thermoset polymers that hold them together. In this Focus Article, we will show the emergence of these structure-focused approaches to CFRP recycling and illustrate the path of this research toward the ultimate realization of methods to recover both the reinforcing fibers and the thermoset materials that comprise modern CFRPs.