  Many-body physics aims to understand emergent properties of systems made of
many interacting objects. This article reviews recent progress on the topic of
radiative heat transfer in many-body systems consisting of thermal emitters
interacting in the near-field regime. Near-field radiative heat transfer is a
rapidly emerging field of research in which the cooperative behavior of
emitters gives rise to peculiar effects which can be exploited to control heat
flow at the nanoscale. Using an extension of the standard Polder and van Hove
stochastic formalism to deal with thermally generated fields in $N$-body
systems, along with their mutual interactions through multiple scattering, a
generalized Landauer-like theory is derived to describe heat exchange mediated
by thermal photons in arbitrary reciprocal and non-reciprocal multi-terminal
systems. In this review, we use this formalism to address both transport and
dynamics in these systems from a unified perspective. Our discussion covers:
(i) the description of non-additivity of heat flux and its related effects,
including fundamental limits as well as the role of nanostructuring and
material choice, (ii) the study of equilibrium states and multistable states,
(iii) the relaxation dynamics (thermalization) toward local and global
equilibria, (iv) the analysis of heat transport regimes in ordered and
disordered systems comprised of a large number of objects, density and range of
interactions, and (v) the description of thermomagnetic effects in
magneto-optical systems and heat transport mechanisms in non-Hermitian
many-body systems. We conclude this review by listing outstanding challenges
and promising future research directions.

Mesoscale and Nanoscale Physics