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.