Spreading depression (SD) is a pathological phenomenon of the central nervous system in which normal cellular function is disrupted by a prolonged depolarization, which spreads spatially at a rate of several millimeters per minute. SD is connected to a number of medical conditions, including migraine with aura, traumatic brain injury, and epilepsy. This thesis presents a general framework for modeling spreading depression as a multiphasic continuum that is based on fully incorporating biophysical principles, including electrodiffusion and osmosis. The generality of the model allows us to explore how many different aspects of the physiology may impact the system, which we do through four specific models. In particular, we explore the effects of fluid flow within the extracellular space, adding a glial compartment, and including two neuronal compartments in one spatial dimension. In addition, we explore features of SD propagation in two spatial dimensions. In each of these four specific models, we vary several different parameters to understand the role they have in the initiation and propagation of SD. We find that many aspects of the system affect the speed of propagation and that glial cells play a significant role in the extracellular potential variation seen during SD. Additionally, some parameters affect the relative timing of the various changes that take place during SD.