This review by David Mattingly, published in *Living Reviews in Relativity*, focuses on modern experimental tests of Lorentz invariance, motivated by theoretical suggestions that Lorentz invariance may not hold at all energies. The review covers both theoretical frameworks for testing Lorentz invariance and experimental advances that have enabled high-precision tests. It presents current constraints on Lorentz-violating effects from terrestrial experiments and astrophysical observations. The article begins with an introduction to the importance of Lorentz invariance in relativity and the theoretical motivations for testing it, including quantum gravity models and other high-energy physics frameworks. It discusses the different types of Lorentz violation, such as systematic and non-systematic violations, and the role of other symmetries like CPT invariance, supersymmetry, and Poincaré invariance. The review then delves into various kinematic frameworks for Lorentz violation, including modified dispersion relations, the Robertson–Mansouri–Sexl (RMS) framework, the $c^2$ framework, and doubly special relativity (DSR). Each framework is described in detail, along with its implications for experimental tests. The experimental sections of the review cover terrestrial experiments such as Penning traps, clock comparison experiments, cavity experiments, spin-polarized torsion balances, and particle physics experiments. It also discusses astrophysical constraints, including time-of-flight measurements, birefringence, threshold interactions, and gravitational observations. Finally, the review concludes with a discussion of the implications of Lorentz violation for gravitational waves, cosmology, and parameterized post-Newtonian (PPN) parameters, and provides an outlook on future progress in the field.This review by David Mattingly, published in *Living Reviews in Relativity*, focuses on modern experimental tests of Lorentz invariance, motivated by theoretical suggestions that Lorentz invariance may not hold at all energies. The review covers both theoretical frameworks for testing Lorentz invariance and experimental advances that have enabled high-precision tests. It presents current constraints on Lorentz-violating effects from terrestrial experiments and astrophysical observations. The article begins with an introduction to the importance of Lorentz invariance in relativity and the theoretical motivations for testing it, including quantum gravity models and other high-energy physics frameworks. It discusses the different types of Lorentz violation, such as systematic and non-systematic violations, and the role of other symmetries like CPT invariance, supersymmetry, and Poincaré invariance. The review then delves into various kinematic frameworks for Lorentz violation, including modified dispersion relations, the Robertson–Mansouri–Sexl (RMS) framework, the $c^2$ framework, and doubly special relativity (DSR). Each framework is described in detail, along with its implications for experimental tests. The experimental sections of the review cover terrestrial experiments such as Penning traps, clock comparison experiments, cavity experiments, spin-polarized torsion balances, and particle physics experiments. It also discusses astrophysical constraints, including time-of-flight measurements, birefringence, threshold interactions, and gravitational observations. Finally, the review concludes with a discussion of the implications of Lorentz violation for gravitational waves, cosmology, and parameterized post-Newtonian (PPN) parameters, and provides an outlook on future progress in the field.