  We study non-linear sigma models with N local supersymmetries in three
space-time dimensions. For N=1 and 2 the target space of these models is
Riemannian or Kahler, respectively. All N>2 theories are associated with
Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it
generally decomposes into two separate quaternionic spaces, associated with
inequivalent supermultiplets. For N=5,6,8 there is a unique (symmetric) space
for any given number of supermultiplets. Beyond that there are only theories
based on a single supermultiplet for N=9,10,12 and 16, associated with coset
spaces with the exceptional isometry groups $F_{4(-20)}$, $E_{6(-14)}$,
$E_{7(-5)}$ and $E_{16(+8)}$, respectively. For $N=3$ and $N\geq5$ the $D=2$
theories obtained by dimensional reduction are two-loop finite.
