Materials modelling of extended defects in requires both  a detailed electronic model of matter to account for bond breaking and formation at the atomic scale and a representation of material systems at large scales, in the micrometre–microsecond range. These twin demands, if implemented directly by ab initio calculations, are unachievable with potentially available computational resources for the foreseeable future.

An alternative approach is to develop multiscale simulations, where the level of simulation detail can vary in time and space, thus saving on computational cost without sacrificing the necessary detailed modelling. This paper introduces the basic concepts and reviews some progress in this field, and the related challenges along two main strands:

(i) sequential multiscale modelling to construct largerscale material models from first principles and

(ii) hybrid multiscale modelling for the description of unitary systems which are too large for monoscale modelling at the desired accuracy.