  In this note we give a concise review of the present state-of-art for the
problem of self-adjoint realisations for the Dirac operator with a Coulomb-like
singular scalar potential $V(\vec x)=\phi(\vec x) I_4$. We try to follow the
historical and conceptual path that leads to the present understanding of the
problem and to highlight the techniques employed and the main ideas. In the
final part we outline a few major open questions that concern the topical
problem of the multiplicity of self-adjoint realisations of the model, and
which are worth addressing in the future.
