The physics of colloidal suspensions confined in slits and cavities has significantly advanced during the last twenty years. In particular, freezing transitions in confinement have been addressed by theory and simulations and experimental realizations were proposed to confine colloidal particles to two dimensions. After reviewing this progress, we discuss the generalization to time-dependent confinement which leads to nonequilibrium situations. This is elaborated further for unstable situations where the particles can leave the confinement. In particular, the completely overdamped Brownian motion of a colloidal particle in a time-dependent harmonic trap is considered. The analytically soluble model of a time-dependent quadratic potential is used to extract the dynamical properties of the potential if the potential undergoes periodic switching from a confining harmonic potential to an unstable one. The amplitudes of the oscillating particle response can strongly grow in time, which we refer to as 'giant breathing'. This giant breathing process occurs also in anharmonic potentials and is verifiable in real-space experiments of colloids in laser-optical fields.