  White dwarf stars constitute the final evolutionary stage for more than 95
per cent of all stars. The Galactic population of white dwarfs conveys a wealth
of information about several fundamental issues and are of vital importance to
study the structure, evolution and chemical enrichment of our Galaxy and its
components ---including the star formation history of the Milky Way. In
addition, white dwarfs are tracers of the evolution of planetary systems along
several phases of stellar evolution. Also, white dwarfs are used as
laboratories for astro-particle physics, being their interest focused on
physics beyond the standard model. The last decade has witnessed a great
progress in the study of white dwarfs. In particular, a wealth of information
of these stars from different surveys has allowed us to make meaningful
comparison of evolutionary models with observations. While some information
like surface chemical composition, temperature and gravity of isolated white
dwarfs can be inferred from spectroscopy, and the total mass and radius can be
derived as well when they are in binaries, the internal structure of these
compact stars can be unveiled only by means of asteroseismology, an approach
based on the comparison between the observed pulsation periods of variable
stars and the periods predicted by appropriate theoretical models. The
asteroseismological techniques allow us to infer details of the internal
chemical stratification, the total mass, and even the stellar rotation profile.
In this review, we first revise the evolutionary channels currently accepted
that lead to the formation of white-dwarf stars, and then, we give a detailed
account of the different sub-types of pulsating white dwarfs known so far,
emphasizing the recent observational and theoretical advancements in the study
of these fascinating variable stars.
