Cortical spreading depression (CSD) has been the focus of intensive experimental and theoretical study since its discovery by Leao in 1944. The connection between CSD waves and migraine with aura and other pathological conditions has made the mathematical study of CSD even more compelling. The quantitative study of CSD has led to mathematical models that incorporate many of the mechanisms known to affect CSD speed, shape, and duration. CSD involves the movement of the major ions (potassium, sodium, chloride, and calcium) in the brain. These ions are trans- ported by diffusion and can go through cell membranes as a result of ionic membrane channels and energy consuming pumps that restore the ionic concentrations to homeostasis. The massive variations in ion concentrations associated with CSD waves also give rise to significant osmotic effects and puts intense stress on the neurovascular coupling that regulates oxygen supply to the brain. In this talk, we will give an overview of the models that have been proposed with a focus on the models for instigation and spreading of SD.