Thanks to the last decades of X-ray observations, the picture of an apparently heterogeneous zoo of isolated neutron stars is emerging. In the attempt of reaching an unified vision of their different phenomenological classes, a key issue is the proper modeling of the cooling and spin-down history of the isolated neutron stars. The sample of about fourty isolated neutron stars that clearly show thermal emission in their X-ray spectra is presented. I compare their timing and spectral properties with the results of our 2D code that simulates for the first time the long-term coupled thermal and magnetic evolution of isolated, magnetised neutron stars.