  Nonlinear sigma models arise in supergravity theories with or without matter
couplings in various dimensions and they are important in understanding the
duality symmetries of M-theory. With this motivation in mind, we review the
salient features of gauged and ungauged nonlinear sigma models with or without
Wess-Zumino terms for general target spaces in a minimal as well as lifted
formulation. Relevant to the question of finding interesting vacua of gauged
supergravity theories is the highly constrained potential which arises
naturally in these theories. Motivated by this fact, we derive a general and
simple formula for a gauge invariant potential of this kind.
