Neural-Network quantum states (NQS) have been recently proposed as a method to solve challenging interacting quantum problems. During this talk, I will discuss the application of NQS to two problems. First, we use a deep convolutional network to find the ground state of the frustrated J1-J2 model on the square lattice. While early representations of many-body quantum states in terms of neural networks are usually based on shallow architectures such as the restricted Boltzmann machine, the benefits of deeper architectures are emerging in the latest research. Here, we show that these deep convolutional NQS can achieve results that are competitive with other state of the art variational methods developed in the past decade. Second, we present an extension of NQS to model interacting fermionic problems. Borrowing techniques from quantum simulation, we directly map fermionic degrees of freedom to spin ones, and then use NQS to perform electronic structure calculations. On small test molecules, we achieve energies below chemical accuracy, and frequently improves upon coupled cluster methods. *The Flatiron Institute is supported by the Simons Foundation. A.M. acknowledges support from the IBM Research Frontiers Institute. KC was supported by the European Unions Horizon 2020 research and innovation program (ERC-StGNeupert-757867-PARATOP).