This review provides a comprehensive survey of recent work on modified theories of gravity and their cosmological implications. It covers a wide range of theories, including General Relativity, Scalar-Tensor, Einstein-Aether, Bimetric, TeVeS, $f(R)$, higher-order theories, Hořava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions such as Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. The review also discusses attempts to construct a Parameterised Post-Friedmannian (PPF) formalism to constrain deviations from General Relativity in cosmology and compare with large-scale data. These subjects have seen rapid progress over the past decade, driven by advancements in observational cosmology, which now allow for precision tests of fundamental physics on the scale of the observable universe. The purpose of this review is to serve as a reference tool for researchers and students in cosmology and gravitational physics, providing a self-contained, comprehensive, and up-to-date introduction to the subject.This review provides a comprehensive survey of recent work on modified theories of gravity and their cosmological implications. It covers a wide range of theories, including General Relativity, Scalar-Tensor, Einstein-Aether, Bimetric, TeVeS, $f(R)$, higher-order theories, Hořava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions such as Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. The review also discusses attempts to construct a Parameterised Post-Friedmannian (PPF) formalism to constrain deviations from General Relativity in cosmology and compare with large-scale data. These subjects have seen rapid progress over the past decade, driven by advancements in observational cosmology, which now allow for precision tests of fundamental physics on the scale of the observable universe. The purpose of this review is to serve as a reference tool for researchers and students in cosmology and gravitational physics, providing a self-contained, comprehensive, and up-to-date introduction to the subject.