This expository paper is an overview of a relatively new class of failure models, both univariate and multivariate, that are suitable for describing the lifelength of items that operate in dynamic environments. Many of the currently used failure models are developed under the premise that the operating environment is static: these models turn out to be special cases of the new models that are overviewed here. These new models are derived by describing the underlying failure-causing mechanisms, such as degradation and wear, using suitable stochastic processes: this is the underlying mathematical theme that derives their development. Because of their generality, the new models should provide improved descriptions of failure data and assessments of item survivability. Furthermore, they may signal a new philosophy of life-testing experiments wherein one also monitors the environmental factors that govern the tests. This overview categorizes the models by the various strategies used for their development, outlines the salient assumptions underlying them and provides a convenient road map to the pertinent references, which are scattered among the applied probability, engineering, reliability and survival analysis literatures. It is our hope that this paper sets a tone for the direction of future work in the development of models for survival wherein the physics of failure and the characteristics of the operating environment play a key role.