  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.
