The impact of time-dependent density-functional theory (TDDFT) in quantum chemistry and materials sciences continues to grow, as evidenced by its increasing use on a widening range of applications. TDDFT has achieved an unprecedented balance between accuracy and efficiency for calculations of the excitation spectra and response of molecules, biomolecules, and solids. Recent years have seen adventurous explorations of non-adiabatic electron-ion dynamics in photochemical reactions, mechanisms of solar cell devices, molecular conductance through nanostructures, viscosity arising from electron-interaction, strong-field processes such as high-harmonic generation, and even optimal control at the attosecond time-scale. Although the theory is an exact reformulation of the quantum dynamics of interacting many-body systems, how well it works in practice in these applications depends on approximations for exchange-correlation effects. Significant progress has been made in recent years as to the understanding of when the usual approximations are expected to work well and when they are expected to fail, especially in the linear response regime, and there is intense on-going research in developing more accurate approximations. The purpose of this 2013 Gordon Research Conference is to bring together developers and users of TDDFT, to discuss the most recent advances, the most pressing challenges, as well as new directions for development and applications. The friendly, open, and lively atmosphere that has prevailed in our previous conferences will foster constructive scientific exchanges throughout the week, both in the discussions following talks, poster sessions, and more informally. 2013 is a particularly special year for TDDFT, resonating with the 90th birthday of Walter Kohn, the 70th birthday of John Perdew, and the 60th birthday of Hardy Gross.