  We consider the exotic vortex equations on compact Riemann surfaces. These
generalise the well-known Jackiw-Pi and Ambj{\o}rn-Olesen vortex equations and
arise as equations for Bogomolny-Prasad-Sommerfield-like configurations in
nonrelativistic Chern-Simons-matter theories. We show that (exotic) vortex
solutions in $U(N)$ gauge theories with a single fundamental flavour on compact
Riemann surfaces can be constructed from gauged holomorphic maps into complex
space forms of dimension $N$. We conjecture, with some evidence, that all such
solutions arise this way. This leads us to insights regarding the moduli theory
of exotic vortices, including the identification of interesting selection rules
for nonAbelian exotic vortices on the sphere. We also consider the classical
and quantum dynamics of exotic vortices. Using recent localisation results, we
give the Witten index of the quantum mechanics describing low-temperature
Abelian exotic vortex dynamics.
