Neuromorphic computing has been gaining momentum for the past decades and has been appointed as the replacer of the outworn technology in conventional computing systems. Artificial neural networks (ANNs) can be composed by memristor crossbars in hardware and perform in-memory computing and storage, in a power, cost and area efficient way. In optoelectronic memristors (OEMs), resistive switching can be controlled by both optical and electronic signals. Using light as synaptic weigh modulator provides a high-speed non-destructive method, not dependent on electrical wires, solving crosstalk issues. In particular, in artificial visual systems, OEMs can act as the artificial retina and combine optical sensing and high-level image processing. Therefore, several efforts have been made by the scientific community into developing OEMs that can meet the demands of each specific application. 
In this Review, the recent advances on inorganic OEMs are summarized and discussed. The engineering of the device structure provides the means to manipulate RS performance and, thus, a comprehensive analysis is performed regarding the already proposed memristor materials structure and their specific characteristics. Moreover, their potential applications in logic gates, ANNs and, in more detail, on artificial visual systems are also assessed, taking into account the figures of merit described so far.