  A general theoretical framework that incorporates possible CPT and Lorentz
violation in an extension of the standard model and in quantum electrodynamics
has been developed over the last decade. The framework originates in the idea
that CPT and Lorentz symmetry could be broken spontaneously in a more
fundamental theory such as string theory. These symmetry violations are
described in the standard-model extension by small terms in the Lagrangian.
Various experiments can bound these quantities. They include Penning-trap
experiments with electrons and positrons, Penning-trap experiments with protons
and antiprotons, and possible experiments with hydrogen and antihydrogen in
traps or beams. I will review aspects of the theory, outline estimated bounds
attainable in specific experiments, and present known bounds from completed
experiments.
