An overall view of key problems in algorithmic trading and recent progress

We summarize the fundamental issues at stake in algorithmic trading, and the progress made in this field over the last twenty years. We first present the key problems of algorithmic trading, describing the concepts of optimal execution, optimal placement, and price impact. We then discuss the most recent advances in algorithmic trading through the use of Machine Learning, discussing the use of Deep Learning, Reinforcement Learning, and Generative Adversarial Networks.