  In this review we define and discuss metastates, mathematical tools with
general applicability to thermodynamic systems which are particularly useful
when working with disordered or inhomogeneous short-range systems. In an
infinite such system there may be many competing thermodynamic states, which
can lead to the absence of a straightforward thermodynamic limit of local
correlation functions. A metastate is a probability measure on the
infinite-volume thermodynamic states that restores the connection between those
states and the Gibbs states observed in finite volumes. After introducing the
basic metastates and discussing their properties, we present possible scenarios
for the spin-glass phase and discuss what the metastate approach reveals about
how replica symmetry breaking would manifest itself in finite-dimensional
short-range spin glasses.
