Kinetic and thermodynamic compensations have been reported in many chemical, physical, biological and food processes. Kinetic compensation can be found for any process and when it takes place, it gives information about the reaction mechanism and whether the reaction is controlled by enthalpy or entropy. It consists of the linear relationship between the logarithm of the frequency factor (lnk0) and the activation energy (Ea), both previously obtained from the Arrhenius equation for different values of an environmental variable (e.g. pH, concentration of any substance not involved in the process, pressure, water activity, etc.). A mathematical consequence of kinetic compensation is the isokinetic temperature, this being the temperature at which the kinetic constant should be the same regardless of the environmental variable. Thermodynamic compensation can be found for any process involving an equilibrium and consists of the linear relationship between the variation of enthalpy and entropy, both previously obtained from the Van't Hoff equation for different values of an environmental variable. A mathematical consequence of thermodynamic compensation is the isoequilibrium temperature, this being the temperature at which the equilibrium constant should be the same regardless of the environmental variable. According to the transition state theory, some kinetic constants can be related to the equilibrium constant of the initial equilibrium stage between the reagents and the transition state. For these cases, it can be concluded that both compensations are related mathematically and therefore not only does the existence of one kind of compensation imply the existence of the other, but the isokinetic and isoequilibrium temperatures should both be the same, or at least very close to each other. However, there is no reason that forces the linearities that cause either kind of compensation. So, some processes have shown these linear relationships while others have not. Moreover, some authors have reported that, due to the fact that the estimates of the parameters for the couples lnk0-Ea and ΔH≠-ΔS≠ being correlated with each other, there is a statistic compensation that consists of the propagation of experimental errors, and this effect has to be considered before concluding kinetic and/or thermodynamic compensations. This work reviews how to deal with kinetic and thermodynamic compensations physically, mathematically and statistically, prior to a second part that reviews the food processes for which one or both of these compensations have been studied.