  The quality, depth, and multi-color nature of the Hubble Deep Field images
makes them an excellent resource for studying galaxies at z > 2 using selection
techniques based on the presence of the 912A Lyman break. I present a
descriptive review of this method and of the properties of the objects which it
identifies, and summarize spectroscopic progress on galaxies with 2 < z < 4 in
the HDF. Using ground-based and HDF samples of Lyman break galaxies I discuss
the luminosity function of galaxies at z ~ 3, and consider the effects of
extinction on the star formation rates that are derived from the UV luminosity
information. Infrared observations of the HDF provide data on the rest-frame
optical properties of z ~ 3 galaxies, which are briefly described.
