Wherever advanced materials are required for technology theory and simulation have a vital role to play. That role may be in making a safety case, or reducing costs by narrowing down the selection of materials, or predicting and preventing failures. It may also be to establish whether and how materials may be designed to meet engineering specifications, or to interpret experimental characterizations of materials over a range of length and time scales.The need for this DTC cannot be overstated: there are no longer PhD graduates produced anywhere in the UK with a foundation knowledge of theoretical and computational materials physics. Current PhD graduates in theory and simulation of materials (TSM), with a first degree in a subject other than materials science, know extremely little about materials physics beyond the topic of their own research. On the other hand very few students with a first degree in materials science have sufficient training in mathematical techniques to engage in TSM at any level beyond the use of standard simulation packages. The need for breadth in the training of PhD graduates in TSM stems directly from the multi-scale and multi-physics nature of the vast majority of challenging problems in materials technology. The need exists both in industrial and academic research. The education and training provided by the DTC will be unique in the UK. For the first time in decades students will be taught theoretical materials physics at a sophisticated mathematical level, which will enable them to model the principal classes of materials across the length and time scales. They will also learn about the principal techniques of simulating materials at different length and time scales, and how information is transferred up and down the length and time scale hierarchies. The multidisciplinary training and research environment of the DTC, in combination with a wide range of cohort building and student empowerment activities, will provide a far richer educational and professional experience than a standard PhD funded through the DTA. The scientific network students will be able to form through the DTC with their peers, academics, industrialists and leading visiting scientists will be a lasting benefit for them.The DTC will bring together key staff of 4 departments across 2 faculties at Imperial College. Students will have 2 supervisors, whose expertise will not be centred at the same length scale. This will usually mean that their supervisors are in different departments. Similarly, no single department has the expertise to provide the range of courses that students will receive in their first year. For these reasons the multidisciplinary training and research environment can be delivered only through a DTC. Conversely, if the DTC is not funded then narrowly focused PhDs in TSM will continue to be generated with the same limited usefulness for industry, academe and the students themselves as they have in the past 2-3 decades.With nuclear power once again a key component of the Government strategy for energy there will be a significant demand from this sector for graduates of the DTC, as confirmed by the letter of support from UKAEA. Other forms of producing energy such as wind and solar power will also benefit. But TSM is needed in all advanced materials technologies, including aerospace and land-based transportation, building and construction, the processing, storage and communication of information, sport, prostheses and health-care, sensors and security, defence and more. The need from academic groups in the UK and overseas is also very significant. Indeed the absence of suitably trained PhD graduates is universally recognised in the attached letters of support from academics, national labs and industry, as one of their principal concerns. Judging by these letters the 50 graduates of the DTC funded by EPSRC are likely to be in very strong demand.