Artificial neural networks have proven to be a flexible tool to compactly represent quantum many-body states in condensed matter, chemistry, and nuclear physics problems, where non-perturbative interactions are prominent. In this talk, I will focus on neural quantum states suitable to solve the many-body Schrödinger equation in a systematically improvable fashion. Because of their favorable polynomial computational cost in the number of particles, neural quantum states enable quantum Monte Carlo calculations of medium-mass nuclei. Applications to their dynamics, relevant for microscopic calculations of neutrino-nucleus scattering, will be discussed.