We present a new uniqueness result for solutions to Fokker–Planck–Kolmogorov (FPK) equations for probability measures on infinite-dimensional spaces. We consider infinite-dimensional drifts that admit certain finite dimensional approximations. In contrast to most of the previous work on FPK-equations in infinite dimensions, we include cases with non-constant coefficients in the second order part and also include degenerate cases where these can even be zero, i.e. we prove uniqueness of solutions to continuity equations. Also new existence results are proved. Applications to proving well-posedness of Fokker–Planck–Kolmogorov equations associated with SPDEs and of continuity equations associated with PDE are discussed. Joint work with Vladimir Bogachev, Giuseppe Da Prato and Stanislav Shaposhnikov