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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.
We use a large $N$-body simulation to study the relation of the structural properties of dark matter halos to their assembly history and environment. The complexity of individual halo assembly histories can be well described by a small number of prin
Using estimates of dark halo masses from satellite kinematics, weak gravitational lensing, and halo abundance matching, combined with the Tully-Fisher and Faber-Jackson relations, we derive the mean relation between the optical, V_opt, and virial, V_
Satellite galaxies in rich clusters are subject to numerous physical processes that can significantly influence their evolution. However, the typical L* satellite galaxy resides in much lower mass galaxy groups, where the processes capable of alterin
We investigate the ability of basis function expansions to reproduce the evolution of a Milky Way-like dark matter halo, extracted from a cosmological zoom-in simulation. For each snapshot, the density of the halo is reduced to a basis function expan
We use the Evolution and Assembly of GaLaxies and their Environments ( EAGLE ) suite of hydrodynamical cosmological simulations to measure offsets between the centres of stellar and dark matter components of galaxies. We find that the vast majority (