Abstract: Artificial Intelligence is nowadays an ubiquitous concept, with a remarkable impact in every field of science and technology. Despite this, a clear understanding of information processing phenomena in neural networks and a comprehensive theoretical basis for it are still missing. In this talk, I will frame the topic of Machine Learning in the language of spin-glass theory for which rigorous statistical-mechanics techniques are available. I will discuss applications of these methods to paradigmatic models of Artificial Intelligence, such as the Hopfield model and the Deep Boltzmann Machine. The results presented can provide a starting point towards a mathematical control of state-of-the-art machine-learning networks.