Cosmological hydrodynamic simulations now routinely incorporate many of the physical processes relevant for studying the bulk of matter in between galaxies. This is in contrast to the theoretical picture for the formation of galaxies themselves which is still very uncertain. Fortunately, what lies between galaxies can be observed in exquisite detail as absorption lines in quasar spectra. In this talk, I will show how we can use knowledge gained from simulations to analyze these quasar spectra. It turns out that next to the Cosmic Microwave Background, the forest of hydrogen Lyman-alpha absorption lines offers possibly the simplest laboratory for studying matter clustering, and will enable us to make precise measurements on much smaller scales, those directly relevant to galaxy formation. I will review the various cosmological uses this information can be put to, which range from constraining the matter density, and the neutrino mass, to testing to gravitational instability theory and the nature of the initial fluctuations. I will then present new results from a large sample of Keck quasar spectra. I will also speculate how the existence of another possible component of the intergalactic medium, diffuse intergalactic dust, might be detected, and how current observations of supernovae at high redshift may provide constraints on the properties of any such dust as well as on cosmology.