  We present a pedagogical review of the halo model, a flexible framework that
can describe the distribution of matter and its tracers on non-linear scales
for both conventional and exotic cosmological models. We start with the premise
that the complex structure of the cosmic web can be described by the sum of its
individual components: dark matter, gas, and galaxies, all distributed within
spherical haloes with a range of masses. The halo properties are specified
through a series of simulation-calibrated ingredients including the halo mass
function, non-linear halo bias and a dark matter density profile that can
additionally account for the impact of baryon feedback. By incorporating a
model of the galaxy halo occupation distribution, the properties of central and
satellite galaxies, their non-linear bias and intrinsic alignment can be
predicted. Through analytical calculations of spherical collapse in exotic
cosmologies, the halo model also provides predictions for non-linear clustering
in beyond-$\Lambda$CDM models. The halo model has been widely used to model
observations of a variety of large-scale structure probes, most notably as the
primary technique to model the underlying non-linear matter power spectrum. By
documenting these varied and often distinct use cases, we seek to further
coherent halo model analyses of future multi-tracer observables. This review is
accompanied by the release of pyhalomodel:
https://github.com/alexander-mead/pyhalomodel , flexible software to conduct a
wide range of halo-model calculations.
