Ionic liquids have attracted a great deal of attention as media for chemical processes, but many fundamental questions about their behavior remain unanswered. Their electrostatic character remains particularly mysterious, and a number of theoretical studies have attempted to address it using various models. These models often make use of a dipolar description of the charge distribution of an ion, or the dielectric continuum model for the medium. In this work, we review these approaches and show that their application to ionic liquids is questionable on fundamental physical grounds. While not formally incorrect, the descriptions are prone to certain conceptual or numerical errors when applied to molecular ionic systems. We highlight these problems, and discuss some alternative approaches currently in the literature.