High-precision experiments could reveal small previously unseen differences between the behavior of matter and antimatter. This prospect is appealing to physicists because it may show that nature is not Lorentz symmetric. Introduction Ordinary matter is made up of protons, electrons, and neutrons. The quantum behavior of these particles can be predicted with excellent accuracy using the Dirac equation, named after P.A.M. Dirac. One of the triumphs of the Dirac equation is its prediction of the existence of antimatter particles. Antiprotons, positrons, and antineutrons are now well understood, and can be created and studied in experiments. High-precision experiments have been unable to detect any difference between the masses of particles and those of the corresponding antiparticles. They also have been unable to detect any difference between the magnitudes of the charges, or between the lifetimes, of particles and antiparticles. These mass, charge, and lifetime symmetries are required in a Lorentz and CPT symmetric universe, but are only a small number of the properties that need to match if the universe is Lorentz and CPT symmetric. The Standard-Model Extension (SME), a comprehensive theoretical framework for Lorentz and CPT violation, makes specific predictions about how particles and antiparticles would behave differently in a universe that is very close to, but not exactly, Lorentz symmetric. In loose terms, the SME can be visualized as being constructed from fixed background fields that interact weakly, but differently, with particles and antiparticles. The behavioral differences between matter and antimatter are specific to each individual experiment. Factors that determine the behavior include the particle species involved, the electromagnetic, gravitational, and nuclear fields controlling the system. Furthermore, for any Earth-bound experiment, the rotational and orbital motion of the Earth is important, leading to sidereal and seasonal signals. For experiments conducted in space, the orbital motion of the craft is an important factor in determining the signals of Lorentz violation that might arise. To harness the predictive power of the SME in any specific system, a calculation has to be performed so that all these factors can be accounted for. These calculations are facilitated by the reasonable assumption that Lorentz violations, if they exist, are small. This makes it possible to use perturbation theory to obtain results that would otherwise be extremely difficult to find. The SME generates a modified Dirac equation that breaks Lorentz symmetry for some types of particle motions, but not others. It therefore holds important information