  The idea that local Lorentz invariance might be violated due to new physics
that goes beyond the Standard Model of particle physics and Einstein's General
Relativity has received a great deal of interest in recent years. At the same
time, new experiments have been designed and conducted that are able to test
Lorentz symmetry at unprecedented levels. Much of this theoretical and
experimental progress has been driven by the development of the framework for
investigating Lorentz violation known as the Standard Model Extension (SME).
The SME is the lagrangian-based effective field theory that by definition
contains all Lorentz-violating interaction terms that can be written as
observer scalars involving particle fields in the Standard Model and
gravitational fields in a generalized theory of gravity. This includes all
terms that could arise from a process of spontaneous Lorentz violation as well
as terms that explicitly break Lorentz symmetry. In this article, an overview
of the SME is presented, including its motivations and construction. A very
useful minimal version of the SME in Minkowski spacetime that maintains gauge
invariance and power-counting renormalizability is constructed as well. Data
tables summarizing tests of local Lorentz invariance for the different particle
sectors in the Standard Model and with gravity are maintained by Kosteleck\'y's
group at Indiana University. A partial survey of these tests, including some of
the high-precision sensitivities they attain, is presented here.
