Thin-film solar cells based on organic semiconductors have attracted considerable attention during the last two decades. Although great improvements have been achieved in the performance of such organic photovoltaic diodes, there are still some issues that are not fully understood. One of these issues is the current of the solar cell in dark, which has been a heavily debated topic in recent years. Here, we demonstrate that the dark current of a solar cell contains important information on charge transport and recombination. From the low-voltage regime of the dark current-voltage characteristics, the diode ideality factor can be determined. It is shown that the diode ideality factor is influenced by diffusion of charge carriers, for which an analytical charge-transport model is presented. In addition, the ideality factor may be enhanced by the presence of trap-assisted recombination. However, we demonstrate that experimental artifacts can complicate correct determination of the ideality factor. Above the built-in voltage of the solar cell, the dark current is limited by the buildup of space charge. We demonstrate how bimolecular recombination affects the space-charge density and, as a result, the dark current. The bimolecular recombination strength can be directly inferred from the dark current by the use of a simple analytical expression. As the bimolecular recombination rate is currently not well understood, this simple steady-state method to probe bimolecular recombination is eminently suitable for screening charge recombination in new materials for organic solar cells.