The covalent bond, a difficult concept to define precisely, plays a central role in chemical predictions, interventions, and explanations. I investigate the structural conception of the covalent bond, which says that bonding is a directional, submolecular region of electron density, located between individual atomic centers and responsible for holding the atoms together. Several approaches to constructing molecular models are considered in order to determine which features of the structural conception of bonding, if any, are robust across these models. Key components of the structural conception are absent in all but the simplest quantum mechanical models of molecular structure, seriously challenging the conception’s viability.