Compact Models (CMs) for circuit simulation have been at the heart of CAD tools for bridging circuit design and technology development over the past decades.  In this talk, we begin with an overview of the historical role of CMs and fundamental equations.  Evolution of MOSFET CMs, from bulk to SOI and FinFETs, is reviewed and their inter-relationships discussed.  Unification of CMs with the unified regional modeling (URM) approach is presented, together with model validation with numerical data and verification with experimental data.  Model extension to III-V HEMTs including 2-dimensional electron gas (2DEG) in multiple sub-bands and trap-charge effects is presented.