White dwarf stars are the most common endpoint of stellar evolution. Therefore, these old, numerous and compact objects provide valuable information on the late stages of stellar evolution, the physics of dense plasma and the structure and evolution of our Galaxy. The ESA Gaia space mission has revolutionized this research field, providing parallaxes and multi‐band photometry for nearly 360,000 white dwarfs. Furthermore, this data, combined with spectroscopical and spectropolarimetric observations, have provided new information on their chemical abundances and magnetic fields. This large data set has raised new questions on the nature of white dwarfs, boosting our theoretical efforts for understanding the physics that governs their evolution and for improving the statistical analysis of their collective properties. In this article, I summarize the current state of our understanding of the collective properties of white dwarfs, based of detailed theoretical models and population synthesis studies.