Although it a very narrow angle survey, the depth of the HDF results in its sampling a significant volume of the halo of our galaxy. Thus it is useful for the purposes of detecting (or placing upper limits on the distribution of) intrinsically faint stars, such as white dwarfs. White dwarfs could provide a significant fraction of the total mass of the halo of the Milky Way. Constraints on the population of halo white dwarfs from the HDF can directly address this possible partial explanation of the nature of the dark halo of the Milky Way. In this review, I illustrate how the HDF can be used to constrain the luminosity function of halo white dwarfs. I begin with a brief summary of the observed white dwarf luminosity function (WDLF) of the galactic disk, and show how the HDF serves as a probe of the WDLF for the halo. I then review the theoretical background used in interpreting the WDLF in terms of the theory of white dwarf evolution and cooling, and the history of star formation in the galaxy. We are then in a position to explore the theoretical WDLF of the disk. and then the halo. The results of searches for white dwarfs on the HDF can then be examined in terms of the halo white dwarf population.