White dwarfs represent the final stage of the life cycle of more than 95% of all stars. These stellar remnants are essentially devoid of energy sources and are thus condemned to cool continuously over billions of years. Thanks to this property, white dwarfs act as "cosmic clocks" and hold a wealth of information on the history of the Galaxy. In recent years, the Gaia mission has increased the number of known white dwarfs tenfold and has provided an exceptionally detailed picture of the local population. In particular, unexpected features have been identified in the Gaia HR diagram of nearby white dwarfs, revealing significant gaps in our understanding of these objects. In this talk, I will present the latest modelling efforts aimed at filling these gaps, and I will show that the Gaia HR diagram can be elegantly explained by the transport of chemical elements in white dwarfs. On one hand, the bifurcation of the white dwarf sequence into two main branches can be attributed to the convective dredge-up of carbon in objects with helium-dominated envelopes. On the other hand, the accumulation of high-mass white dwarfs at a specific location in the HR diagram is the result of a distillation process triggered by the crystallisation of the carbon-oxygen core. Distillation gives rise to a very efficient downward transport of neutron-rich impurities (such as neon-22), which releases a large amount of gravitational energy and thus interrupts the cooling for billions of years. This phenomenon had been never observed in any type of stars before and challenges our very notion of white dwarfs as dead stars.