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This tutorial paper addresses the problems and solutions that are posed by the design of mixed-signal integrated systems on chip (SoC). These include problems in mixed-signal design methodologies and flows, problems in analog design productivity, as well as open problems in analog, mixed-signal and RF design, modeling and verification tools. The tutorial explains the problems that are posed by these mixed-signal/RF SoC designs, describes the solutions and their underlying methods that exist today and outlines the challenges that still remain to be solved at present. In the first part the design of analog and mixed-signal circuits is addressed, while the second part focuses on the specific problems raised by RF wireless circuits.