An understanding of the white dwarf stars is central to much of astrophysics, from the structure and evolution of stars to the age and history of the large ensembles of stars that we call galaxies. They are of great potential interest from the standpoint of physics as well, because they offer a chance to study matter under extreme conditions not yet attainable in the laboratory. White dwarfs are the simplest kinds of star that we know of, yet they are still very complicated. There are a number of questions that we must answer in order to understand them and the physics that governs their behaviour. Here I describe how we can use asteroseismology to answer these questions. I give a quick introduction to the field, summarize what has been done, and describe what looks promising for the future.