The following figure shows the generic phase diagram of hole-doped cuprate materials. The balance between the different phases is controlled by the temperature T and the charge carrier doping p. The undoped material (p=0) is an antiferromagnetic Mott-insulator. Mott insulators are different from usual band insulator where Pauli exclusion principle is responsible for the insulating character. In a Mott insulator, Coulomb repulsion, which prevents two electrons to occupy the same atomic site on a crystal lattice, forces one charge carrier to localize on each atomic site. In such an arrangement, the lowest energy spin configuration is obtained when next nearest neighbours interact antiferromagnetically so that electron spin orders in a pattern of successive spin up and down. Upon doping, this antiferromagnetic phase vanishes rapidly and superconductivity emerges. The maximum critical temperature Tc is obtained at the optimal carrier doping (p 0.16). The overdoped regime is defined as the region of the phase diagram where the doping is higher than optimal doping. In this regime, Tc decreases with doping and electronic properties are considered as those of a Fermi liquid (a correlated metal). On the other hand, the underdoped regime, defined for dopings below optimal doping, hosts of a very peculiar phase : the pseudogap phase, which is at the center of an intense debate since its discovery more than 20 years ago. The underdoped regime and the pseudogap phase are our favourite playground for our research in high magnetic field.