Recent cosmological observations have suggested that the universe is under- going accelerated expansion. This can not be explained within the framework of General Relativity and the Standard Model of particle physics, which has been dubbed the dark energy problem. In this thesis, we study the possibility that dark energy originates from modifications of General Relativity on very large scales. The Gauss-Bonnet term arises naturally in string theory as a higher order correction to the Einstein-Hilbert term. Upon compactification to 4 dimensions, it can give rise to 1(9) gravity, 9 being the 4D Gauss-Bonnet term. We reduce a general 1(9) model in the FRW background to an autonomous system, via which we systematically classify general 1(9) models. As a result, easy-to-use criteria are employable to check whether a given 1(9) model can produce a viable background evolution. Galileon modified gravity, in which modifications to General Relativity are encoded in a scalar field called the galileon, is motivated by certain braneworld scenarios. One simple example is the Dvali-Gabadadze-Porrati model, where the brane bending mode plays the role of the galileon in the decoupling limit. Unlike the DGP model, ghost-free self-accelerating branches can exist in general galileon models. We study the multi-field generalisation of the galileon model. By an explicit example, we show that a higher eo-dimensional braneworld model can give rise to an effective 4D theory with multiple galileons. We find that certain multi-galileon models are phenomenologically healthier than the single galileon model, and admit self-tuning backgrounds where the gravitational effects of a (small) cosmological constant can be dynamically cancelled away, which is an explicit example of degravitation. We argue that the effective galileon field theory can have an internal symmetry if the underlying braneworld model has certain geometric symmetry in the bulk, and explicitly construct models with the SO(N) and SU(N) fundamental and ad- joint symmetries. Also, we find that in symmetric multi-galileon models a generic self-accelerating vacuum will spontaneously break the internal symmetry, whose pattern can be described by a variant of Goldstone's theorem. Observationally, this may be reflected in tests of gravity on very large scales.