Energy production from thermonuclear fusion power plants is one of the most ambitious energy projects in the world today. The European fusion roadmap outlines the main steps towards commercial fusion power plants, including the development of the European DEMOnstration Power Plant (DEMO), which will demonstrate the commercial feasibility of fusion power plants.In this context, a crucial component is the divertor which is in charge for power handling and particle exhaust, while operating in a harsh loading environment. The current DEMO divertor is composed of a Cassette Body (CB) supporting two Plasma Facing Components (PFCs). The most promising divertor cooling scheme foresees two separate cooling circuits for the CB and PFCs, provided with cooling water at different operating conditions. Moreover, the divertor design has been recently revised so to operate the CB with a high-temperature and high-pressure coolant. These design assumptions pose new challenges in achieving uniform and effective cooling of the structure to ensure reliable operation for the intended divertor lifetime.The work conducted during the Ph.D. years progressed along parallel paths. In a first phase, the main objective was to numerically assess the steady-state thermo-hydraulic performance of the DEMO divertor cooling circuits. In particular, an integrated fluid-structure Computational Fluid-Dynamic analyses campaign of the entire divertor was carried out introducing new details and a significant increase of complexity with respect to the previous approach adopted for such kind of studies.The twofold aim was to evaluate the CB thermal performance under the revised coolant conditions and to compare the temperature distribution in the PFC's Target Bodies by selecting different materials actually under assessment to extend the component’s lifetime under irradiation. Despite the many advantages connected to the new high temperature divertor, some critical points were identified in terms of thermal hydraulic performances, which pose the need for a design revision of some parts.During a second phase, attention was focused on two peculiar aspects of the thermostructural performance of the DEMO divertor. The first one was the behaviour of the CB structure subjected to the high pressure and its compliance with the structural design code. In this regard, the CB structural response under the load combination foreseen for a hydrostatic test scenario was assessed, showing some interesting outcomes and suggesting a design revision of the internal divertor ribs to improve its structural integrity.Furthermore, the second complementary aspect was the structural behaviour of the plasma-facing surfaces, which are subjected to high thermal and particle fluxes. In particular, the study was applied to a divertor plasma-facing surface which is supposed to be coated with a thin layer of Tungsten. In this framework, a theoretical-numerical assessment of the residual stresses on a typical Tungsten armour was carried out. The main outcome of the activity was the verification that the influence of temperature-dependent mechanical properties of the materials affects the results in a negligible way.