This review presents the current state of research on modified gravity theories beyond the standard ΛCDM model, focusing on how new physics can appear in the gravitational sector and how it can be tested. The review discusses the cosmological constant problem, the need for new physics to explain the observed accelerated expansion of the universe, and the various screening mechanisms that allow new fields to remain undetected in local gravity tests. It categorizes screening mechanisms into three broad classes: those that become active in regions of high Newtonian potential, those where first derivatives of the field are important, and those where second derivatives are important. Examples include chameleon, symmetron, galileon, and massive gravity theories. The review also discusses experimental tests of these theories, including laboratory and solar system tests, as well as astrophysical and cosmological observations. It highlights the importance of effective field theory as a unifying framework for understanding these models and their implications for future tests. The review is structured to be accessible to both theorists and experimentalists, with a focus on the theoretical developments and observational prospects for modified gravity theories.This review presents the current state of research on modified gravity theories beyond the standard ΛCDM model, focusing on how new physics can appear in the gravitational sector and how it can be tested. The review discusses the cosmological constant problem, the need for new physics to explain the observed accelerated expansion of the universe, and the various screening mechanisms that allow new fields to remain undetected in local gravity tests. It categorizes screening mechanisms into three broad classes: those that become active in regions of high Newtonian potential, those where first derivatives of the field are important, and those where second derivatives are important. Examples include chameleon, symmetron, galileon, and massive gravity theories. The review also discusses experimental tests of these theories, including laboratory and solar system tests, as well as astrophysical and cosmological observations. It highlights the importance of effective field theory as a unifying framework for understanding these models and their implications for future tests. The review is structured to be accessible to both theorists and experimentalists, with a focus on the theoretical developments and observational prospects for modified gravity theories.