The compensation phenomenon in heterogeneous catalysis takes the form of a sympathetic linear correlation between the observed parameters of the Arrhenius equation E-app and ln A(app) for a series of related reactions or catalysts: ln A(app) = mE(app) + c Exact obedience to this Cremer-Constable relation requires all Arrhenius plots in the set to intersect at the isokinetic temperature (T-i). When this is established with statistical rigor (which is rare), the term "isokinetic relationship" (IKR) is used, the term "compensation" being reserved for cases in which this has not been done. Early work suggested that T-i equated to that at which the catalysts were prepared, but this observation has not been generally confirmed. Experimental error in the Arrhenius plots and other causes, such as a change in mechanism or the onset of diffusion limitation, can give rise to false ''apparent'' compensation which is of no real significance. The scope of this review is strictly limited to heterogeneously catalyzed reactions; thermal desorption is excluded. Explanations advanced include (1) distribution of active-site energy and (2) an enthalpy-entropy relation originating either in the thermodynamics of chemisorption, or in the activation parameters of the Transition State Theory, or in the process of energy transfer between initial and final states. The distinction between apparent (E-app and ln A(app)) and true (E-t and In A,) Arrhenius parameters is clearly drawn: The latter are observed only where the catalyst exhibits a high affinity for the adsorbate(s) and where, therefore, the coverage is high and independent of temperature within the range of measurement; zero-order kinetics then apply. Structure insensitivity is often observed under these conditions. Compensation is only seen with apparent Arrhenius parameters, which occur when chemisorption is weaker: The resulting lower coverages are temperature dependent and sensitive to many variables such as catalyst composition and the nature of the reactant(s). Reaction orders are then greater than zero, and under these conditions, structure sensitivity is often found. Values of E-t then exceed those of E-app by the appropriate adsorption enthalpy terms. Model calculations based on Langmuir-Hinshelwood bimolecular kinetics show that compensation may occur within a single system, due simply to a change of coverage with reactant pressure: Consequential changes in the exponential term exp(-E-app/RT) are greater than changes in rate, so that compensation is inevitable. These concepts are illustrated by reference to three systems: (1) acid-catalyzed hydrocarbon transformations, where independent measurements of adsorption enthalpies are available; (2) metal-catalyzed hydrogenation of benzene and its homologs, where mathematical modeling extracts values for E-t and adsorption enthalpies; and (3) metal-catalyzed hydrogenolysis of alkanes, where the endothermic initial C-H bond splitting causes the value of E-app to be larger than E-t, thus explaining inter alia the variation of E-app with chain length. If, in a set of reaction systems, conditions far measuring the temperature dependence of rate are chosen such that adsorbed reactant concentrations vary to an appreciable degree, values of E-app will necessarily differ, and compensation will appear if accompanying changes in rate are small (i.e., if T-i lies within or close to the temperature range used).