We discuss how simulations of mechanical properties of materials require descriptions at many different length scales -- from the nanoscale where an atomic description is appropriate, through a mesoscale where dislocation based descriptions may be useful, to macroscopic length scales. In some materials, such as nanocrystalline metals, the range of length scales is compressed and a polycrystalline material may be simulated at the atomic scale. The first part of the paper describes such simulations of nanocrystalline copper. We observe how the grain boundaries contribute actively to the deformation. At grain sizes below 10-15nm deformation in the grain boundaries dominate over the traditional dislocation-based deformation mechanisms. This results in a reversal of the normal grain size dependence of the yield stress: we observe that the material becomes softer when the grain size is reduced. The second part of the paper gives an overview over simulation techniques appropriate for problems too large to be treated in atomic-scale simulations. It also describes how different simulation techniques can be combined to describe the interplay between phenomena at different length scales through multiscale modelling.