The measurement of the dark I-V curve is one of the most straightforward methods for characterizing solar cells. Consequently, an accurate knowledge of its meaning is of high relevance for the comprehension and technological feedback of these devices. In this paper, an explanation of the dark I-V curve for concentrator III-V solar cells is presented using a 3D (three-dimensional) model in order to provide a proper data fit that provides meaningful physical parameters that are also compatible and coherent with a data fit from illumination curves. The influence on the dark I-V curve of the most significant series resistance components of concentrator solar cells is also analysed concluding that only the vertical component as well as the front contact-specific resistance can be assessable by means of this characterization method while both emitter and metal sheet resistances cannot be detected. For comparison purposes, the same experimental data have been fitted by means of a traditional two-diode model showing that, although an accurate dark I-V curve fitting can be achieved, the extracted parameters are unable to reproduce illumination data since lumped models assume the same ohmic losses distribution for both dark and illumination conditions.