Compact MOSFET models are a critical link between technology and design. The inexorable reduction in supply voltage and geometry to 45nm and below adds or emphasizes physical effects not important in the past, and so continues to expand the requirements for MOSFET models. At and below 45nm, process variations, reliability, proximity effects, high-k gate materials, and non-classical device structures all challenge modeling. This tutorial presents fundamentals and evolution of compact MOSFET models, and techniques to address the new challenges.