A quantum transport-based analysis of the essential physics of carrier capture in semiconductor quantum wells is presented. First, the past progression of models of carrier capture by quantum wells is briefly reviewed. Then carrier capture is modeled using the Schrödinger Equation Monte Carlo (SEMC) quantum transport simulator. In addition to reproducing familiar effects, these simulations exhibit significant effects associated with partial phase-coherence of the carrier wave-function across the well which cannot be modeled via classical or perturbative Golden Rule calculations, and address fundamental transport limitations often overlooked in Golden Rule calculations. However, this analysis also points to simple changes that could significantly improve, although not perfect, the treatment of carrier capture via these latter more conventional approaches.