  Copious star formation occurs in the dense Central Molecular Zone (CMZ) of
our Galaxy, but at a much smaller rate than occurs in a comparable mass of
molecular gas in the Galactic disk. The combination of large turbulent velocity
dispersions, a relatively strong magnetic field, and a strong tidal field all
contribute to inhibiting star formation (SF) in different ways in different CMZ
locations. Nonetheless, there are spectacular displays of recent and ongoing SF
in the CMZ, including massive young stellar clusters, sites of abundant SF in
progress, and numerous spots of protostellar or YSO activity. The presence of
giant molecular clouds in the CMZ that are almost entirely devoid of SF
indicates that SF requires a trigger that is not present everywhere. The
dominant provocation of SF is likely to be cloud compression, either by
large-scale shocks or by orbital motion of clouds into a region of enhanced
tidal compression and/or enhanced external pressure. Recent hypotheses for
where and how SF takes place in the CMZ are constrained by the recent orbital
determinations of the massive Arches and Quintuplet clusters. Star formation in
the central parsec is subject to a very different set of physical conditions,
and is less well understood, but is important for the co-evolution of the
central black hole and the nuclear star cluster.
