Essential elements of thermolytic reaction kinetics for distributions of polymers are reviewed. Bond scission, occurring randomly along a chain backbone or at the chain end, is the major reaction process in polymer thermolysis. Underlying this bond scission are free radical mechanisms, including initiation and termination, hydrogen abstraction, and beta scission. Population-balance equations for the molecular-weight distributions of macromolecules or their radicals describe the dynamics of the reactions. The governing integrodifferential equations for continuous distributions can be solved by moment methods, similarity techniques, other analytical procedures, or numerical methods. The approach has been applied to analytical thermolysis and pyrolysis, polymer degradation for stability characterization or plastics recycling, and coal thermolysis to produce fuels and feedstocks. Experiments have demonstrated the usefulness of the continuous distribution kinetics approach for polymer thermolysis with additives, including hydrogen donors, peroxides, and other polymers. Molecular-weight distributions and their moments can be measured by size exclusion chromatography. Experimental data can be interpreted by evaluating rate parameters, which may be composites of rate coefficients for elementary steps in complex reaction mechanisms.