  There are various types of global and local spacetime invariant in general
relativity. Here I focus on the local invariants obtainable from the curvature
tensor and its derivatives. The number of such invariants at each order of
differentiation that are algebraically independent will be discussed. There is
no universally valid choice of a minimal set. The number in a complete set will
also be discussed. The invariants can then be used to characterize solutions of
the Einstein equations (locally), to test apparently distinct solutions for
equivalence, and to construct solutions. Other applications concern limits of
families of spacetimes, and the characterization of horizons and singularities.
Further uses are briefly mentioned.
