The aim of this seminar is to explain, to a wide audience, how to combine optimal control techniques with reinforcement learning, by using approximate dynamic programming, and artificial neural networks, to obtain adaptive optimal controllers. Although with roots since the end of the XX century, this problem has been the subject of an increasing attention. In addition to the promising tools that it offers to tackle difficult nonlinear problems with major engineering importance (ranging from robotics to biomedical engineering and beyond), it has the charm of creating a meeting point between the control and machine learning research communities.