Solving the quantum many-body problem entails non-trivial difficulties arising from the exponential growth of the Hilbert space dimension. Artificial neural networks have proven to be a flexible tool for compactly representing quantum many-body states in problems of condensed matter, chemistry, and nuclear physics, where non-perturbative interactions are prominent. I will present on a variational Monte Carlo method based on neural-network quantum states that solves the nuclear Schrödinger equation in a systematically improvable fashion with a polynomial cost in the number of nucleons. In addition to atomic nuclei and nucleonic matter, I will present applications to condensed matter systems, such as the homogeneous electron gas and strongly interacting ultra-cold Fermi gases near the unitary limit. Perspectives on accessing the real-time dynamics of quantum many-body systems will also be discussed.