In 2018, an international Task Force (TF) dedicated to the ITER Disruption Mitigation System (DMS) has been formed. The present paper summarizes Theory and Modelling (T&M) activities performed within this TF. The ITER DMS is planned to rely on Shattered Pellet Injection (SPI). The most critical issue, at present, is that of Runaway Electrons (REs). Indeed, recent T&M work suggests that previously envisaged means of RE avoidance or mitigation may prove inefficient. However, RE simulations have not yet taken into account the possibly beneficial role of magnetohydrodynamic (MHD) instabilities. Furthermore, new promising schemes for RE avoidance or mitigation are being investigated. These comprise, among others: 1) a prompt plasma dilution before the disruption by means of pure H2 SPI in order to suppress hot tail RE generation, and 2) should a RE beam form, a “cleanout” of the beam’s companion plasma, via (again) pure H2 SPI into the beam, which may lead to a benign beam termination. The paper also discusses the status of 3D MHD modelling. The JOREK, M3D-C1 and NIMROD codes have been extended in recent years to be able to simulate SPI. Good cooperation exists between the 3 teams, which materializes for example in useful benchmarks. Code validation on present experiments is progressing hand-in-hand with physics understanding. Predictions for ITER, although still at an early stage, suggest that multiple SPI may be an efficient way to limit radiation asymmetries. Substantial 3D MHD modelling work is also ongoing in the areas of vertical displacement events, halo currents and electromagnetic loads. Finally, integrated modelling shows that material deposition from SPI will strongly depend on the target plasma, suggesting that SPI parameters may need to be adapted to the latter. SPI for disruption mitigation poses new questions in terms of detailed pellet physics, which will be outlined.