High-Tc cuprate superconductors have the highest known superconducting critical temperature at ambient pressure. Their phase diagram features several baffling mysteries. The basic questions we are trying to answer are: what is the organizing principle of the phase diagram of high-Tc cuprates? what is the mechanism for high-Tc superconductivity? We use high magnetic fields to suppress superconductivity in order to reach and determine the nature of the electronic interactions at play in the phase diagram and in the pairing mechanism of those systems.