Classical density functional theory (DFT) has been proven to be a powerful mathematical tool to describe the equilibrium structure and phase behavior of correlated many-body systems (e.g., dense colloidal or biological fluids) in bulk or under the action of external potentials. Using the equilibrium functional a dynamic DFT can be constructed which accurately reproduces the strongly inhomogeneous steady-state or even time-dependent structure of systems in non-equilibrium. This talk aims at a pedagogical introduction exemplified by simple colloidal systems out of equilibrium, such as colloidal sedimentation, diffusion-controlled reactions, and driven polymer solutions.