In this tutorial, we shall briefly review two of the main workhorses of modern machine learning: neural networks and stochastic gradient descent. We shall also review recent developments of machine learning methods and theory for stochastic control and games, with applications to financial models. The focus is on the approximation capabilities of deep neural networks, viewed as a powerful tool to overcome the curse of dimensionality, to compute the optimal strategies in stochastic control problems or find Nash equilibria in multi-agent games, and mean-field games in high dimensions with complex structures. If time allows, we will also talk about state-of-the-art works done at the crossroad of artificial intelligence and stochastic control and games, identifying unsolved challenges, and connecting to real applications.