Hazard models are often applied to mortality data of humans and other species so that the parameter estimates made for those models can be used to make inferences about the biology, and comparative biology, of aging processes. Enough longitudinal data on physiological and functional changes in humans now exist to know that the age trajectory of the physiological state of individuals is multidimensional, stochastic, and plastic. Thus, to fully assess the biological significance of existing longitudinal data on human aging and mortality processes, multivariate stochastic process models must be developed that are biologically detailed and valid. This requires assessing genetic mechanisms controlling human longevity and rates of aging, developing models of how those traits may have evolved, and developing statistical methods for identifying gene environment interactions. This article examines the theoretical basis for such models and the biological rationale of their parametric structure. Several examples are given.