Understanding and modelling the static charge decay on an insulating material surface have been the topic of numerous research works since the nineteenth century. After an introduction on this historical context, a selection is presented here covering the various phenomena that may be held responsible for the decay: ion deposit from the surrounding atmosphere, charge injection and transport through the conduction and trapping levels of the solid, internal polarization by free carrier motion or dipole polarization, as well as surface conduction and migration of the deposited charge along the surface. Surface potential measurements are a convenient technique to study these various types of charge motion but the underlying complexity concerning their interpretation is often neglected. Depending on the context, the law of electrostatics may produce a hyperbolic as well as an exponential decay. On an insulating polymer, or any other disordered insulator, charge transport is dispersive, and conduction as well as dipolar polarization responses are described by time power laws. The knowledge of this time response is not sufficient to build a convincing physical model, because of the universality of this response, which leaves many degrees of freedom to interpret the data. Knowledge of the possible elementary processes and their signatures in the observables is therefore requested before the implementation of curve-fitting procedures.