The formulation and some experimental implications of a general Lorentz-violating extension of the standard model are reviewed. The theory incorporates both CPT-preserving and CPT-breaking terms. It is otherwise a conventional quantum field theory, obtained under the assumption that Lorentz symmetry is spontaneously broken in an underlying model. The theory contains the usual standard-model gauge structure, and it is power-counting renormalizable. Energy and momentum are conserved. Despite the violation of Lorentz symmetry, the theory exhibits covariance under Lorentz transformations of the observer inertial frame. A general Lorentz-violating extension of quantum electrodynamics can be extracted. The standard-model extension implies potentially observable effects in a wide variety of experiments, including among others measurements on neutral-meson oscillations, comparative studies in Penning traps, spectroscopy of hydrogen and antihydrogen, bounds on cosmological birefringence, measurements of muon properties, clock-comparison tests, and observations of the baryon asymmetry.