The last decade has seen a rapid increase in the number of precision tests of relativity. This research has been motivated by the intriguing possibility that tiny deviations from relativity might arise in the underlying theory that is widely believed to successfully mesh General Relativity (GR) with quantum physics. Many of these tests have been analyzed within an effective field theory framework which generically describes possible deviations from exact relativity and contains some traditional test frameworks as limiting cases. One part of the activity has been a resurgence of interest in tests of relativity in the Minkowski-spacetime context, where Lorentz symmetry is the key ingredient. Numerous experimental and observational constraints have been obtained on many different types of relativity deviations involving matter. Another part, which has developed more recently, has seen the effective field theory framework extended to include the curved spacetime regime, and recent theoretical work within this framework has shown that there are many unexplored ways in which the foundations of GR can be tested. Qualitatively new signals for deviations from local Lorentz symmetry involving lunar laser ranging observations and atom interferometry experiments have already been analyzed within this framework, and many exciting new possibilities exist for future work including proposed Weak Equivalence Principle (WEP) tests.