Computational materials science has been progessing at a substantial rate over the last few decades. Classical computers have proven suitable to tackle a range of problems in materials science. In the near future, however, we may reach the limits of what is possible with classical computers, particularly taking into account the energy needs of large scale computation. Quantum computers offer an exciting opportunity to meet significant new challenges far beyond the realms of possibility using classical CPUs. In this talk I outline a set of problems that face computational materials scientists, with the aim of forming a dialogue between materials scientists and experts in quantum computation.