Modeling is essential to simulate the operation of integrated circuit (IC) before its fabrication. Seeing a large number of Metal-Oxide-Silicon Field-Effect-Transistor (MOSFET) models available, it has become important to understand them and compare them for their pros and cons. The task becomes equally difficult when the complexity of these models becomes very high. The paper reviews the mainstream models with their physical relevance and their comparisons. Major short-channel and quantum effects in the models are outlined. Emphasis is set upon the latest compact models like BSIM, MOS Models 9/11, EKV, SP etc.