Comet nuclei are very difficult to observe and no direct data of the interior are at present available: theoretical models of the chemical differentiation and thermal evolution of a nucleus are still necessary to link coma observations with real nuclei properties. They can be used to: 1) give initial conditions to coma models, explaining observations in terms of surface and internal processes and nucleus composition; 2) foresee dust and gas fluxes and surface thermal characteristics on the basis of assumed nucleus conditions; 3)test theories explaining particular phenomena (crust formation, splitting, fluxes dependence on various parameters) and hypotheses on the nature of cometary materials. After a pioneering phase following the Giotto mission, these kind of models rapidly evolved in the last years, under the impulse of planned space missions (such as Rosetta and Stardust) and the effect provided by the presence of extraordinary comets. The comparison between the results of models and the observations of Shoemaker-Levy-9, Hyakutake and Hale-Bopp is pushing the modellers to try to account for several complex and interacting phenomena observed on the targets.\\ In this talk we will review the present state of these models, stressing on physical processes accounted for and on what should constitute the "frontier" (realistic crust formation, multi-dimensional models and so on). In the last part of this talk, we would like to stress out the impact that different assumptions on initial parameters (such as, for example, composition and properties of the cometary matter) can have on the output of nucleus models, showing once more the importance of laboratory experiments.