Solving the quantum many-body problem entails non-trivial difficulties stemming from the exponential growth of the Hilbert space dimension. 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. I will focus on a variational Monte Carlo method based on neural-network quantum states that solves the nuclear SchrÃ¶dinger equation in a systematically improvable fashion with a polynomial cost in the number of nucleons. In addition to the nuclear many-body problem, I will present applications to condensed-matter systems, such as the homogeneous electron gas and strongly interacting cold Fermi gases. Perspectives on accessing the real-time dynamics of quantum many-body systems will also be discussed.