White Dwarfs are extremely common endpoints of stellar evolution, and their ubiquity makes them excellent laboratories for probing many topics in astrophysics. In isolation they cool peacefully and predictably, with pure atmospheres that result in clean spectra. Material from stellar or planetary companions can pollute these otherwise clean spectra, turning white dwarfs into laboratories for studying the nature and composition of their surroundings. In this talk, I will focus on the theoretical work necessary to infer properties of exoplanetary systems and debris disks using polluted white dwarf spectra. I will also discuss connections between polluted white dwarf atmospheres and supernova explosions, where newly emerging classes of highly polluted high velocity objects appear to be remnants associated with Type Ia(x) supernovae. This highlights the need for more theoretical work on white dwarf evolution to enable interpretation of the wealth of white dwarf data in the era of Gaia and beyond.