Having been inspired by the tremendous progress in material nanoscience and device nanoengineering, hybrid phototransistors combine solution processed colloidal semiconductor quantum dots (QDs) with graphene or two-dimensional (2D) semiconductor materials. Novel detectors demonstrate ultrahigh photoconductive gain, high and selective photoresponse, low noise, and very high responsivity in visible- and near-infrared ranges. The outstanding performance of phototransistors is primarily due to the strong, selective, and size tunable absorption of QDs and fast charge transfer in 2D high mobility conductors. However, the relatively small mobility of QD nanomaterials was a technological barrier, which limited the operating rate of devices. Very recent innovations in detector design and significant progress in QD ligand engineering provide effective tools for further qualitative improvements. This article reviews the recent progress in material science, nanophysics, and device engineering related to hybrid phototransistors. Detectors based on various QD nanomaterials and several 2D conductors are compared, and advantages and disadvantages of various nanomaterials for applications in hybrid phototransistors are identified. We also benchmark the experimental characteristics with model results that establish interrelations and tradeoffs between detector characteristics, such as responsivity, dark and noise currents, the photocarrier lifetime, response, and noise bandwidths. We have shown that the most recent phototransistors demonstrate performance limited by the fundamental generation recombination noise in high gain devices. Interrelation between the dynamic range of the detector and the detector sensitivity is discussed. The review is concluded with a brief discussion of the remaining challenges and possible significant improvements in the performance of hybrid phototransistors.