Real-time time-dependent functional theory (RT-TDDFT) directly propagates the electron density in the time domain by integrating the time-dependent Kohn–Sham equations. This is in contrast to the popular linear response TDDFT matrix formulation that computes transition frequencies from a ground state reference. RT-TDDFT is, therefore, a potentially powerful technique for modeling atto- to picosecond electron dynamics, including charge transfer pathways, the response to a specific applied field, and frequency dependent linear and nonlinear properties. However, qualitatively incorrect electron dynamics and time-dependent resonant frequencies can occur when perturbing the density away from the ground state due to the common adiabatic approximation. An overview of the RT-TDDFT method is provided here, including examples of some cases that lead to this qualitatively incorrect behavior. © 2016 Wiley Periodicals, Inc.