Lenka Zdeborová - Commissariat à l'Énergie Atomique (CEA) The affinity between statistical physics and machine learning has long history, this is reflected even in the machine learning terminology that is in part adopted from physics. I will describe the main lines of this long-lasting friendship in the context of current theoretical challenges and open questions about deep learning. Theoretical physics often proceeds in terms of solvable synthetic models, I will describe the related line of work on solvable models of multi-layer neural network, and their current limitations. In a second part I will follow with related inference tools for learned neural networks and some of their applications.