Modern searches for Lorentz violation are scientific studies that look for deviations from Lorentz invariance or symmetry, a set of fundamental frameworks that underpin modern science and fundamental physics in particular. These studies try to determine whether violations or exceptions might exist for well-known physical laws such as special relativity and CPT symmetry, as predicted by some variations of quantum gravity, string theory, and some alternatives to general relativity. Lorentz violations concern the fundamental predictions of special relativity, such as the principle of relativity, the constancy of the speed of light in all inertial frames of reference, and time dilation, as well as the predictions of the standard model of particle physics. To assess and predict possible violations, test theories of special relativity and effective field theories (EFT) such as the Standard-Model Extension (SME) have been invented. These models introduce Lorentz and CPT violations through spontaneous symmetry breaking caused by hypothetical background fields, resulting in some sort of preferred frame effects. This could lead, for instance, to modifications of the dispersion relation, causing differences between the maximal attainable speed of matter and the speed of light. Both terrestrial and astronomical experiments have been carried out, and new experimental techniques have been introduced. No Lorentz violations have been measured thus far, and exceptions in which positive results were reported have been refuted or lack further confirmations. For discussions of many experiments, see Mattingly (2005). For a detailed list of results of recent experimental searches, see Kostelecký and Russell (2008–2013). For a recent overview and history of Lorentz violating models, see Liberati (2013). Assessing Lorentz invariance violations Early models assessing the possibility of slight deviations from Lorentz invariance have been published between the 1960s and the 1990s. In addition, a series of test theories of special relativity and effective field theories (EFT) for the evaluation and assessment of many experiments have been developed, including: The parameterized post-Newtonian formalism is widely used as a test theory for general relativity and alternatives to general relativity, and can also be used to describe Lorentz violating preferred frame effects. The Robertson-Mansouri-Sexl framework (RMS) contains three parameters, indicating deviations in the speed of light with respect to a preferred frame of reference. The c2 framework (a special case of the more general THεμ framework) introduces a modified dispersion relation and describes Lorentz violations in terms of a discrepancy between the speed of light and the maximal attainable