Special emphasis is placed on the physical processes that lead to the formation of white dwarfs as well as on the different energy sources and processes responsible for chemical abundance changes that occur along their evolution. We enumerate the reasons that make these stars excellent chronometers, and we describe why white dwarfs provide tools for a wide variety of applications. In this work, we review the essentials of the physics of white dwarf stars. These potential applications of white dwarfs have led to renewed interest in the calculation of very detailed evolutionary and pulsational models for these stars. In particular, white dwarfs can be used to constrain fundamental properties of elementary particles such as axions and neutrinos and to study problems related to the variation of fundamental constants. Last but not least, since many white dwarf stars undergo pulsational instabilities, the study of their properties constitutes a powerful tool for applications beyond stellar astrophysics. In addition, the high densities and temperatures characterizing white dwarfs allow these stars to be used as cosmic laboratories for studying physical processes under extreme conditions that cannot be achieved in terrestrial laboratories. In particular, white dwarfs can be used as independent reliable cosmic clocks, and can also provide valuable information about the fundamental parameters of a wide variety of stellar populations, such as our Galaxy and open and globular clusters. Thus, the study of white dwarfs has potential applications in different fields of astrophysics. Since the coolest white dwarfs are very old objects, the present population of white dwarfs contains a wealth of information on the evolution of stars from birth to death, and on the star formation rate throughout the history of our Galaxy. White dwarf stars are the final evolutionary stage of the vast majority of stars, including our Sun.