Pulsars are rapidly spinning neutron stars, that radiate at the expense of their strong magnetic field and their high surface temperature. Five decades of multi-wavelength observations showed a large variety of physical parameters, such as the spin period, the magnetic field and the age, and of observational properties, especially in the radio and X-ray band. Isolated neutron stars have been classified according to the presence of thermal or non-thermal emission, and whether they show a constant flux, rapid flares and bursts or long-standing outbursts. One of the current challenges in the study of such objects is to explain these different manifestations in the context of a unified evolutionary picture. On the other hand, recent findings show that the classes of isolated neutron stars are more connected than previously thought, and that non only magnetars hold a complex magnetic field topology in the crust and above the surface.