Recent advances in computer simulation at the atomic scale have made it possible to probe the structure and behaviour of the cores of dislocations in minerals. Such simulation offers the possibility to understand and predict the dislocation-mediated properties of minerals such as mechanisms of plastic deformation, pipe diffusion and crystal growth. In this review the three major methods available for the simulation of dislocation cores are described and compared. The methods are: (1) cluster-based models which combine continuum elastic theory of the extended crystal with an atomistic model of the core; (2) dipole models which seek to cancel the long-range elastic displacement caused by the dislocation by arranging for the simulation to contain several dislocations with zero net Burgers vector, thus allowing a fully periodic super-cell calculation; and (3) the Peierls-Nabarro approach which attempts to recast the problem so that it can be solved using only continuum-based methods, but parameterizes the model using results from atomic-scale calculations. The strengths of these methods are compared and illustrated by some of the recent studies of dislocations in mantle silicate minerals. Some of the unresolved problems in the field are discussed.