Density functional theory (DFT) is the most widely used electronic structure theory. Crucial to its future is the problem of designing functionals with improved predictive power. I shall describe a new approach to functional design, “survival of the most transferable”, and show how the resulting functionals offer unprecedented accuracy for DFT calculations of intermolecular interactions. As a counterpoint to this vital numerical development, I will discuss the challenge of obtaining physical insight into DFT calculations of intermolecular and intra-molecular interactions. We are aiming to meet this challenge with new energy decomposition analysis (EDA) methods that variationally separate interactions associated with frozen fragment electronic structure, from any spin-coupling, from induced electrostatics, and forward and backwards charge transfer.