  Cosmological observations are beginning to reach a level of precision that
allow us to test some of the most fundamental assumptions in our working model
of the Universe. One such an assumption is that gravity is governed by the
General Theory of Relativity. In this review we discuss how one might go about
extending General Relativity and how such extensions can be described in a
unified way on large scales. This allows us to describe the impact of modified
gravity on the growth and morphology of the large scale structure of the
Universe. On smaller scales we explore the physics of gravitational screening
and how it might manifest itself in galaxies, clusters and, more generally, in
the cosmic web. We then analyze the current constraints from large scale
structure and conclude by discussing the future prospects of the field in light
of the plethora of surveys currently being planned.
