Optimizations have gained much consideration from the researchers working in the domains of analog and radio frequency (RF), recently. Dealing with highly nonlinear behavior of active components and aiming to meet design specifications are common issues in all nonlinear circuit designs. As a consequence and accordingly, many studies have been conducted on diverse optimization methods and algorithms for tackling the design problems and meeting optimal solutions with high accuracy. The main purpose of this article is to provide a comprehensive and systematic literature review for the optimization approaches applied by the researchers for designing various analog and microwave circuits. We focus on considering the existing optimization methods from the newly published optimization methods in the last decade. Thus, this study can guide and enlighten complementary metal-oxide-semiconductor analog and RF microwave circuit designers to consider optimization methods commonly used in both areas and to expand conventional performance figures used in their area.