Molecular simulation may ideally serve as a "computational laboratory", with is ability to observe both structure and dynamics at high resolution and to simulate molecules that are difficult to synthesize. However, it also suffers from fundamental limitations, in particular in the accurate modeling of molecules and in the efficient computation of experimental observables. By leveraging the latest developments in machine learning, we can advance molecular simulation algorithms to make significant progress at these fronts without sacrificing rigorous physics. In this talk, I will give an overview over our work on the highly accurate computation of quantum states with deep fermionic neural networks and Quantum Monte Carlo, and addressing the many-body sampling problem using deep Markov State Models and generative deep learning.