Cosmological Tests of Gravity

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.