The Hubbard model is a paradigm of the `strong correlation problem’, with relevance to high-T_c superconductors and ultra-cold atoms in optical lattices. Key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods working in synergy (such as quantum embedding, tensor networks, various flavors of quantum Monte Carlo and, recently, neural quantum states). I will review some of these recent developments and especially emphasize how the recent development of Neural Quantum States allows to address the question: Does the Hubbard model host a high-Tc superconducting phase?