Time-dependent density-functional theory (TDDFT) is an approach to the dynamical many-body problem which has become widely used in many areas of physics, chemistry and materials science. This talk gives an overview of the basic formalism of TDDFT and presents applications to atoms and molecules in strong laser fields. We will discuss some of the problems and critical issues of TDDFT for ultrafast, strong-field processes, and present some recent developments in the construction of dynamical exchange-correlation potentials beyond the adiabatic approximation.