After the discovery of neutrino masses by the neutrino oscillation experiments, next frontiers are the discovery of CP violation on the lepton sector, the Majorana nature of neutrinos and the discovery of cosmological neutrinos. I will discuss the current status of the Hyper-Kamiokande experiment, with special focus on the Spanish contributions to the construction of the gigantic detector. I will also discuss the physics potential and challenges in the discovery of neutrinoless double decay and in the observation of cosmological neutrinos.