Accelerated testing is the attempt to accelerate the degradation processes that occur in a material system by applying a high stress. Typically accelerated testing requires extrapolating results from a feasible regime for laboratory or factory experimentation to a natural setting of interest. Usually the models used for this extrapolation either arise from assuming a single rate limiting step in the physical or chemical degradation process or as purely empirical relations. This paper presents a general theory for the design and interpretation of accelerated testing derived by considering a simple theory of how processes may trade off as stress decreases and time increases. Some of the main results of the theory are counter to current accepted practice. In particular, careful step stress experiments (experiments in which stress is perturbed during the accelerated aging) are shown to be necessary for identifying acceleration functions, and the possibility of predicting how long experiments need to be run prior to beginning the experiments is indicated.