We briefly review the current state of the art of microwave CAD technologies. We look into the history of design optimization and CAD-oriented modeling of microwave circuits as well as electromagnetics-based optimization techniques. We emphasize certain direct approaches that utilize efficient sensitivity evaluations as well as surrogate-based optimization approaches that greatly enhance electromagnetics-based optimization performance. On the one hand, we review recent adjoint methodologies, on the other we focus on space mapping implementations, including the original, aggressive, implicit, output, tuning, and related developments. We illustrate our presentation with suitable examples and applications. VC 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE 20:475–491, 2010.