Organic photodetectors (OPDs) have gained increasing interest as they offer cost-effective fabrication methods using low temperature processes, making them particularly attractive for large area image detectors on lightweight flexible plastic substrates. Moreover, their photophysical and optoelectronic properties can be tuned both at a material and device level. Visible-light OPDs are proposed for use in indirect-conversion X-ray detectors, fingerprint scanners, and intelligent surfaces for gesture recognition. Near-infrared OPDs find applications in biomedical imaging and optical communications. For most applications, minimizing the OPD dark current density (Jd) is crucial to improve important figures of merits such as the signal-to-noise ratio, the linear dynamic range, and the specific detectivity (D*). Here, a quantitative analysis of the intrinsic dark current processes shows that charge injection from the electrodes is the dominant contribution to Jd in OPDs. Jd reduction is typically addressed by fine-tuning the active layer energetics and stratification or by using charge blocking layers. Yet, most experimental Jd values are higher than the calculated intrinsic limit. Possible reasons for this deviation are discussed, including extrinsic defects in the photoactive layer and the presence of trap states. This provides the reader with guidelines to improve the OPD performances in view of imaging applications.