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Progress in microelectronic technology is extremely fast and it is outstripping the designers' abilities to make use of the created opportunities. Development and application of new more suitable design methods and tools is therefore very important for the modern system industry. This paper shows the importance of the AI search techniques for the circuits and systems design space exploration, explains what sorts of search techniques are useful for this aim, and discusses the place, role and way of use of these techniques in circuit and system design. In particular, the paper explains the importance and usage of the heuristic search techniques for the automatic construction and selection of the most promising solutions to the circuit synthesis problems. The discussion and conclusions of the paper are illustrated with examples of three effective and efficient search algorithms, and experimental results from their application to two important circuit synthesis problems. The knowledge presented in the paper combines numerous valuable concepts of modern system engineering and artificial intelligence, and forms a base for further research and application of the AI search techniques to design of complex circuits and systems.