One of the main characteristics of infinite-dimensional dissipative evolution equations, such as the Navier-Stokes equations, is that their long-time dynamics is determined by finitely many parameters – a finite number of determining modes, nodes, volume elements and other determining interpolants. In this talk I will show how to explore this finite-dimensional feature of the long-time behavior of infinite-dimensional dissipative systems to design finite-dimensional feedback control for stabilizing their solutions. Notably, it is observed that this very same approach can be implemented for designing data assimilation algorithms for weather prediction based on discrete measurements. In addition, I will also show that the long-time dynamics of the Navier-Stokes equations can be imbedded in an infinite-dimensional dynamical system that is induced by an ordinary differential equation, named determining form, which is governed by a globally Lipschitz vector field. The Navier-Stokes equations are used as an illustrative example, and all the above mentioned results equally hold for other dissipative evolution PDEs, in particular for various dissipative geophysical models.