  In this paper we review some recent results on nonlocal interaction problems.
The focus is on interaction kernels that are anisotropic variants of the
classical Coulomb kernel. In other words, while preserving the same singularity
at zero of the Coulomb kernel, they present preferred directions of
interaction. For kernels of this kind and general confinement we will prove
existence and uniqueness of minimisers of the corresponding energy. In the case
of a quadratic confinement we will review a recent result by Carrillo & Shu
about the explicit characterisation of minimisers, and present a new proof,
which has the advantage of being extendable to higher dimension. In light of
this result, we will re-examine some previous works motivated by applications
to dislocation theory in materials science. Finally, we will discuss some
related results and open questions.
