In our modern understanding of galaxy formation, every galaxy forms within a dark matter halo. The formation and growth of galaxies over time is connected to the growth of the halos in which they form. The advent of large galaxy surveys as well as high-resolution cosmological simulations has provided a new window into the statistical relationship between galaxies and halos and its evolution. Here we define this galaxy-halo connection as the multi-variate distribution of galaxy and halo properties that can be derived from observations and simulations. This connection provides a key test of physical galaxy formation models; it also plays an essential role in constraints of cosmological models using galaxy surveys and in elucidating the properties of dark matter using galaxies. We review techniques for inferring the galaxy-halo connection and the insights that have arisen from these approaches. Some things we have learned are that galaxy formation efficiency is a strong function of halo mass; at its peak in halos around a pivot halo mass of 10^12 Msun, less than 20% of the available baryons have turned into stars by the present day; the intrinsic scatter in galaxy stellar mass is small, less than 0.2 dex at a given halo mass above this pivot mass; below this pivot mass galaxy stellar mass is a strong function of halo mass; the majority of stars over cosmic time were formed in a narrow region around this pivot mass. We also highlight key open questions about how galaxies and halos are connected, including understanding the correlations with secondary properties and the connection of these properties to galaxy clustering.
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