  This review presents a comprehensive overview of galaxy bias, that is, the
statistical relation between the distribution of galaxies and matter. We focus
on large scales where cosmic density fields are quasi-linear. On these scales,
the clustering of galaxies can be described by a perturbative bias expansion,
and the complicated physics of galaxy formation is absorbed by a finite set of
coefficients of the expansion, called bias parameters. The review begins with a
detailed derivation of this very important result, which forms the basis of the
rigorous perturbative description of galaxy clustering, under the assumptions
of General Relativity and Gaussian, adiabatic initial conditions. Key
components of the bias expansion are all leading local gravitational
observables, which include the matter density but also tidal fields and their
time derivatives. We hence expand the definition of local bias to encompass all
these contributions. This derivation is followed by a presentation of the
peak-background split in its general form, which elucidates the physical
meaning of the bias parameters, and a detailed description of the connection
between bias parameters and galaxy statistics. We then review the excursion-set
formalism and peak theory which provide predictions for the values of the bias
parameters. In the remainder of the review, we consider the generalizations of
galaxy bias required in the presence of various types of cosmological physics
that go beyond pressureless matter with adiabatic, Gaussian initial conditions:
primordial non-Gaussianity, massive neutrinos, baryon-CDM isocurvature
perturbations, dark energy, and modified gravity. Finally, we discuss how the
description of galaxy bias in the galaxies' rest frame is related to clustering
statistics measured from the observed angular positions and redshifts in actual
galaxy catalogs.
