AbstractThe 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.