  We construct dual Lagrangians for $G/H$ models in two space-time dimensions
for arbitrary Lie groups $G$ and $H\subset G$. Our approach does not require
choosing coordinates on $G/H$, and allows for a natural generalization to
Lie-Poisson duality. For the case where the target metric on $G/H$ is induced
from the invariant metric on $G$, the dual system is a gauged Higgs model, with
a nonconstant metric and a coupling to an antisymmetric tensor. The dynamics
for the gauge connection is governed by a $BF$-term. Lie-Poisson duality is
relevant once we allow for a more general class of target metrics, as well as
for couplings to an antisymmetric tensor, in the primary theory. Then the dual
theory is written on a group $\tilde G$ dual to $G$, and the gauge group $H$
(which, in general, is not a subgroup of $\tilde G$) acts nonlinearly on
$\tilde G$. The dual system therefore gives a nonlinear realization of a gauge
theory. All dual descriptions are shown to be canonically equivalent to the
corresponding primary descriptions, at least at the level of the current
algebra.
