  This chapter reviews the different methodological aspects of the ab ini-tio
modeling of dislocations. Such simulations are now frequently used to study the
dislocation core, i.e. the region in the immediate vicinity of the line defect
where the crystal is so strongly distorted that an atomic description is
needed. This core region controls some dislocation fundamental properties, like
their ability to glide in different crystallographic planes. Ab initio
calculations based on the density functional theory offer a predictive way to
model this core region. Because dislocations break the periodicity of the
crystal and induce long range elastic fields, several specific approaches
relying on different boundary conditions have been developed to allow for the
atomistic modeling of these defects in simulation cells having a size
compatible with ab initio calculations. We describe these different approaches
which can be used to study dislocations with ab initio calculations and
introduce the different analyses which are currently performed to characterize
the core structure, before discussing how meaningful energy properties can be
extracted from such simulations.
