This review provides a comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. It covers General Relativity, Scalar-Tensor, Einstein-Aether, Bimetric theories, TeVeS, $ f(R) $, higher-order theories, Hořava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. The review also discusses attempts to construct a Parameterised Post-Friedmannian formalism to constrain deviations from General Relativity in cosmology and compare with data on the largest scales. These subjects have been intensively studied over the past decade, driven by rapid progress in observational cosmology that now allows precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole. The review begins with an introduction to General Relativity, its foundations, and the requirements for validity. It then discusses the parameterised post-Newtonian approach, cosmology, and the evidence for the $ \Lambda $ CDM model. The review then explores alternative theories of gravity with extra fields, including Scalar-Tensor, Einstein-Ether, Bimetric, and Tensor-Vector-Scalar theories. It also covers higher derivative and non-local theories of gravity, higher dimensional theories of gravity, and parameterised post-Friedmannian approaches and observational constraints. The review concludes with a discussion of the current state of modified gravity theories and their implications for cosmology.This review provides a comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. It covers General Relativity, Scalar-Tensor, Einstein-Aether, Bimetric theories, TeVeS, $ f(R) $, higher-order theories, Hořava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. The review also discusses attempts to construct a Parameterised Post-Friedmannian formalism to constrain deviations from General Relativity in cosmology and compare with data on the largest scales. These subjects have been intensively studied over the past decade, driven by rapid progress in observational cosmology that now allows precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole. The review begins with an introduction to General Relativity, its foundations, and the requirements for validity. It then discusses the parameterised post-Newtonian approach, cosmology, and the evidence for the $ \Lambda $ CDM model. The review then explores alternative theories of gravity with extra fields, including Scalar-Tensor, Einstein-Ether, Bimetric, and Tensor-Vector-Scalar theories. It also covers higher derivative and non-local theories of gravity, higher dimensional theories of gravity, and parameterised post-Friedmannian approaches and observational constraints. The review concludes with a discussion of the current state of modified gravity theories and their implications for cosmology.