Aspects of the theories that are conventionally and widely used for the kinetic analyses of thermal decompositions of solids, crystolysis reactions, are discussed critically. Particular emphasis is placed on shortcomings which arise because reaction models, originally developed for simple homogeneous reactions, have been extended, without adequate justification, to represent heterogeneous breakdowns of crystalline reactants. A further difficulty in the mechanistic interpretation of kinetic data obtained for solid-state reactions is that these rate measurements are often influenced by secondary controls. These include: (i) variations of reactant properties (particle sizes, reactant imperfections, nucleation and growth steps, etc.), (ii) the effects of reaction reversibility, of self-cooling, etc. and (iii) complex reaction mechanisms (concurrent and/or consecutive reactions, melting, etc.). A consequence of the contributions from these secondary rate controls is that the magnitudes of many reported kinetic parameters are empirical and results of chemical significance are not necessarily obtained by the most frequently used methods of rate data interpretation. Insights into the chemistry, controls and mechanisms of solid-state decompositions, in general, require more detailed and more extensive kinetic observations than are usually made. The value of complementary investigations, including microscopy, diffraction, etc., in interpreting measured rate data is also emphasized. Three different approaches to the formulation of theory generally applicable to crystolysis reactions are distinguished in the literature. These are: (i) acceptance that the concepts of homogeneous reaction kinetics are (approximately) applicable (assumed by many researchers), (ii) detailed examination of all experimentally accessible aspects of reaction chemistry, but with reduced emphasis on reaction kinetics (Boldyrev) and (iii) identification of rate control with a reactant vaporization step (L’vov). From the literature it appears that, while the foundations of the widely used model (i) remain unsatisfactory, the alternatives, (ii) and (iii), have not yet found favour. Currently, there appears to be no interest in, or discernible effort being directed towards, resolving this unsustainable situation in which three alternative theories remain available to account for the same phenomena. Surely, this is an unacceptable and unsustainable situation in a scientific discipline and requires urgent resolution?