  In this article we survey and examine the realizability of $p$-groups as
Galois groups over arbitrary fields. In particular we consider various
cohomological criteria that lead to necessary and sufficient conditions for the
realizability of such a group as a Galois group, the embedding problem (i.e.,
realizability over a given subextension), descriptions of such extensions,
automatic realizations among $p$-groups, and related topics.
