This chapter has a twofold purpose. The first is to present an up-to-date review of the basic theoretical and practical aspects of the main reliability models, and of some models that are rarely adopted in literature, although being useful in the authors’ opinion; some very new models, or new ways to justify their adequacy, are also presented. The above aspects are illustrated from a general, methodological, viewpoint, but with an outlook to their application to power system component characterization, aiming at contributing to a rational model selection. Such selection should be based upon a full insight into the basic consequences of assuming—sometimes with insufficient information—a given model. The second purpose of this chapter, closely related to the first, is to highlight the rationale behind a proper and accurate selection of a reliability model for the above devices, namely a selection which is based on phenomenological and physical models of aging, i.e., on the probabilistic laws governing the process of stress and degradation acting on the device. This “technological” approach, which is also denoted in the recent literature as an “indirect reliability assessment” (IRA), might be in practice the only feasible in the presence of a limited amount of data, as typically occurs in the field of modern power system. Although the present contribution does not address, for reasons of brevity, the topic of model or parameter statistical estimation, which is well covered in reliability literature, we believe that the development of the IRA is perfectly coherent—from a “philosophical” point of view—with the recent success and fast-growing adoption of the Bayesian estimation methodology in reliability. In the chapter, first the most adopted reliability models in the literature about electrical components are synthetically reviewed from the viewpoint of the classical “direct reliability assessment”, i.e., a reliability assessment via statistical fitting directly from in-service failure data of components. The properties of these models, as well as their practical consequences, are discussed and it is shown that direct fitting of failure data may result poor or uncertain due to the limited number of data. Thus, practical aids for reliability assessment can be given by the knowledge of the degradation mechanisms responsible for component aging and failure. Such aging and life models, when inserted in a probabilistic framework, lead to “physical reliability models” that are employed for the above-mentioned IRA: in this respect, a key role is played by “Stress-Strength” models, whose properties are discussed in detail in the chapter. Then, since insulation is the weakest part of most electrical devices—particularly in medium voltage and high voltage systems—phenomenological and physical models are developed over the years for the estimation of insulation aging and life is illustrated in this framework. By means of this approach, new derivations of the log-logistic distribution and of the “Inverse power model”, widely ad...