Discotic (disk-shaped) molecules or molecular aggregates may form, within a certain temperature range, partially ordered phases, known as discotic liquid crystals, which have been extensively studied in the recent past. On the one hand, this interest was prompted by the fact that they represent models for testing energy and charge transport theories in organic materials. However, their long-range self-assembling properties, potential low cost, ease of processability with a variety of solvents and the relative ease of tailoring their properties via chemical synthesis, drove the attention of researchers also towards the exploitation of their semiconducting properties in organic electronic devices. This review covers recent research on the charge transport properties of discotic mesophases, starting with an introduction to their phase structure, followed by an overview of the models used to describe charge mobility in organic substances in general and in these systems in particular, and by the description of the techniques most commonly used to measure their charge mobility. The reader already familiar or not interested in such details can easily skip these sections and refer to the core section of this work, focusing on the most recent and significant results regarding charge mobility in discotic liquid crystals.