  We illustrate how the notion of asymptotic coupling provides a flexible and
intuitive framework for proving the uniqueness of invariant measures for a
variety of stochastic partial differential equations whose deterministic
counterpart possesses a finite number of determining modes. Examples exhibiting
parabolic and hyperbolic structure are studied in detail. In the later
situation we also present a simple framework for establishing the existence of
invariant measures when the usual approach relying on the Krylov-Bogolyubov
procedure and compactness fails.
