  We review the current knowledge about nuclear star clusters (NSCs), the
spectacularly dense and massive assemblies of stars found at the centers of
most galaxies. Recent observational and theoretical work suggest that many NSC
properties, including their masses, densities, and stellar populations vary
with the properties of their host galaxies. Understanding the formation,
growth, and ultimate fate of NSCs therefore is crucial for a complete picture
of galaxy evolution. Throughout the review, we attempt to combine and distill
the available evidence into a coherent picture of NSC evolution. Combined, this
evidence points to a clear transition mass in galaxies of ~10^9 solar masses
where the characteristics of nuclear star clusters change. We argue that at
lower masses, NSCs are formed primarily from globular clusters that inspiral
into the center of the galaxy, while at higher masses, star formation within
the nucleus forms the bulk of the NSC. We also discuss the coexistence of NSCs
and central black holes, and how their growth may be linked. The extreme
densities of NSCs and their interaction with massive black holes lead to a wide
range of unique phenomena including tidal disruption and gravitational wave
events. Lastly, we review the evidence that many NSCs end up in the halos of
massive galaxies stripped of the stars that surrounded them, thus providing
valuable tracers of the galaxies' accretion histories.
