The area of catalysis of radical reactions has recently flourished. Various reaction conditions have been discovered and explained in terms of catalytic cycles. These cycles rarely stand alone as unique paths from substrates to products. Instead, most radical reactions have innate chains which form products without any catalyst. How do we know if a species added in "catalytic amounts" is a catalyst, an initiator, or something else? Herein we critically address both catalyst-free and catalytic radical reactions through the lens of radical chemistry. Basic principles of kinetics and thermodynamics are used to address problems of initiation, propagation, and inhibition of radical chains. The catalysis of radical reactions differs from other areas of catalysis. Whereas efficient innate chain reactions are difficult to catalyze because individual steps are fast, both inefficient chain processes and non-chain processes afford diverse opportunities for catalysis, as illustrated with selected examples.