  In this topical review we discuss the nature of the low-temperature phase in
both infinite-ranged and short-ranged spin glasses. We analyze the meaning of
pure states in spin glasses, and distinguish between physical, or
``observable'', states and (probably) unphysical, ``invisible'' states. We
review replica symmetry breaking, and describe what it would mean in
short-ranged spin glasses. We introduce the notion of thermodynamic chaos,
which leads to the metastate construct. We apply these tools to short-ranged
spin glasses, and conclude that replica symmetry breaking, in any form, cannot
describe the low-temperature spin glass phase in any finite dimension. We then
discuss the remaining possible scenarios that_could_ describe the
low-temperature phase, and the differences they exhibit in some of their
physical properties -- in particular, the interfaces that separate them. We
also present rigorous results on metastable states and discuss their connection
to thermodynamic states. Finally, we discuss some of the differences between
the statistical mechanics of homogeneous systems and those with quenched
disorder and frustration.
