The theoretical potential of white dwarf asteroseismology is summarized. It is shown how one can derive fundamental parameters on the internal structure and evolution of these stars. The analysis of the non-radial g-modes permits in principle to determine the total mass, the rotation rate, the magnetic field strength. The mass of the outer layers, left on top of the carbon/oxygen core, can be determined as well as the structure of the transition zone between the core and the outer layers, giving an “a posteriori” unique information on the efficiency of the previous mass loss episodes. When measurable, the rate of change of the pulsation periods gives direct access to the evolutionary time scale and to the chemical composition of the core. These theoretical expectations are compared with the observations of variable white dwarfs in the three known instability strips for the planetary nebulae nuclei and PG1159 stars, for the DB and DA white dwarfs. Emphasis is put on results obtained from multi-sites photometric campaigns. Prospects on both theoretical developments and observations conclude the review.