  The largest gap in our understanding of nature at the fundamental level is
perhaps a unified description of gravity and quantum theory. Although there are
currently a variety of theoretical approaches to this question, experimental
research in this field is inhibited by the expected Planck-scale suppression of
quantum-gravity effects. However, the breakdown of spacetime symmetries has
recently been identified as a promising signal in this context: a number of
models for underlying physics can accommodate minuscule Lorentz and CPT
violation, and such effects are amenable to ultrahigh-precision tests. This
presentation will give an overview of the subject. Topics such as motivations,
the SME test framework, mechanisms for relativity breakdown, and experimental
tests will be reviewed. Emphasis is given to observations involving antimatter.
