  One of the most difficult questions in present-day physics concerns a
fundamental theory of space, time, and matter that incorporates a consistent
quantum description of gravity. There are various theoretical approaches to
such a quantum-gravity theory. Nevertheless, experimental progress is hampered
in this research field because many models predict deviations from established
physics that are suppressed by some power of the Planck scale, which currently
appears to be immeasurably small. However, tests of relativity theory provide
one promising avenue to overcome this phenomenological obstacle: many models
for underlying physics can accommodate a small breakdown of Lorentz symmetry,
and numerous feasible Lorentz-symmetry tests have Planck reach. Such mild
violations of Einstein's relativity have therefore become a focus of recent
research efforts. This presentation provides a brief survey of the key ideas in
this research field and is geared at both experimentalists and theorists. In
particular, several theoretical mechanisms leading to deviations from
relativity theory are presented; the standard theoretical framework for
relativity violations at currently accessible energy scales (i.e., the SME) is
reviewed, and various present and near-future experimental efforts within this
field are discussed.
