While organic electronics is mostly dominated by light-emitting diodes, photovoltaic cells and transistors, optoelectronics properties peculiar to organic semiconductors make them interesting candidates for the development of innovative and disruptive applications also in the field of light signal detection. In fact, organic-based photoactive media combine effective light absorption in the region of the spectrum from ultraviolet to near-infrared with good photogeneration yield and low-temperature processability over large areas and on virtually every substrate, which might enable innovative optoelectronic systems to be targeted for instance in the field of imaging, optical communications or biomedical sensing. In this review, after a brief resume of photogeneration basics and of devices operation mechanisms, we offer a broad overview of recent progress in the field, focusing on photodiodes and phototransistors. As to the former device category, very interesting values for figures of merit such as photoconversion efficiency, speed and minimum detectable signal level have been attained, and even though the simultaneous optimization of all these relevant parameters is demonstrated in a limited number of papers, real applications are within reach for this technology, as it is testified by the increasing number of realizations going beyond the single-device level and tackling more complex optoelectronic systems. As to phototransistors, a more recent subject of study in the framework of organic electronics, despite a broad distribution in the reported performances, best photoresponsivities outperform amorphous silicon-based devices. This suggests that organic phototransistors have a large potential to be used in a variety of optoelectronic peculiar applications, such as a photo-sensor, opto-isolator, image sensor, optically controlled phase shifter, and opto-electronic switch and memory.