This thesis is concerned with the decomposition of intermolecular interaction energies computed by Hartree-Fock theory or Kohn-Sham density functional theory into physically meaningful contributions. While there is no unique way to perform this energy decomposition analysis (EDA), such methods can be judged based on formal properties, physical content, and descriptive power. Throughout this work we assess and address the weaknesses of the Absolutely Localized Molecular Orbital (ALMO) energy decomposition scheme to develop a new scheme with terms describing five distinct physical contributions: permanent electrostatics, Pauli repulsion, exchange-correlation, polarization, and charge transfer. This scheme moreover has many desirable formal properties, satisfying all of the criteria for a good EDA method that we outline in the introduction.