  The vast majority of stars that populate the Universe will end their
evolution as white-dwarf stars. Applications of white dwarfs include
cosmochronology, evolution of planetary systems, and also as laboratories to
study non-standard physics and crystallization. In addition to the knowledge of
their surface properties from spectroscopy combined with model atmospheres, the
global pulsations that they exhibit during several phases of their evolution
allow spying on the deep interior of these stars. Indeed, by means of
asteroseismology, an approach based on the comparison between the observed
pulsation periods of variable white dwarfs and the periods predicted by
representative theoretical models, we can infer details of the internal
chemical stratification, the total mass, and even the stellar rotation profile
and strength of magnetic fields. In this article, we review the current state
of the area, emphasizing the latest findings provided by space-mission data.
