Artificial intelligence is becoming an increasingly popular tool in more and more areas of technology. New challenges in control systems design and application are related to increased productivity, control flexibility, and processing of big data. Some kinds of systems require autonomy in real-time decision-making, while the other ones may serve as an essential factor in human-robot interaction and human influences on system performance. Naturally, the complex tasks of controlling technical systems require new modern solutions, but there remains an inextricable link between control theory and artificial intelligence. The first part of the present survey is devoted to the main intelligent control methods in technical systems. Among them, modern methods of adaptive and optimal control, fuzzy logic, and machine learning are considered. In its second part, the crucial achievements in intelligent control applications in robotic and mechatronic systems over the past decade are considered. The references are structured according to the type of such common control problems as stabilization, controller tuning, identification, parametric optimization, iterative learning, and prediction. In the conclusion, the main problems and tendencies toward intelligent control methods improvement are outlined.