  We review recent developments and results in testing general relativity (GR)
at cosmological scales. The subject has witnessed rapid growth during the last
two decades with the aim of addressing the question of cosmic acceleration and
the dark energy associated with it. However, with the advent of precision
cosmology, it has also become a well-motivated endeavor by itself to test
gravitational physics at cosmic scales. We overview cosmological probes of
gravity, formalisms and parameterizations for testing deviations from GR at
cosmological scales, selected modified gravity (MG) theories, gravitational
screening mechanisms, and computer codes developed for these tests. We then
provide summaries of recent cosmological constraints on MG parameters and
selected MG models. We supplement these cosmological constraints with a summary
of implications from the recent binary neutron star merger event. Next, we
summarize some results on MG parameter forecasts with and without astrophysical
systematics that will dominate the uncertainties. The review aims at providing
an overall picture of the subject and an entry point to students and
researchers interested in joining the field. It can also serve as a quick
reference to recent results and constraints on testing gravity at cosmological
scales.
