Despite the significant progress made in deep learning on digital computers, their energy consumption and computational speed still fall short of meeting the standards for brain-like computing. To address these limitations, reservoir computing (RC) has been gaining increasing attention across communities of electronic devices, computing systems, and machine learning, notably with its in-memory or in-sensor implementation on the hardware–software co-design. Hardware regarded, in-memory or in-sensor computers leverage emerging electronic and optoelectronic devices for data processing right where the data are stored or sensed. This technology dramatically reduces the energy consumption from frequent data transfers between sensing, storage, and computational units. Software regarded, RC enables real-time edge learning thanks to its brain-inspired dynamic system with massive training complexity reduction. From this perspective, we survey recent advancements in in-memory/in-sensor RC, including algorithm designs, material and device development, and downstream applications in classification and regression problems, and discuss challenges and opportunities ahead in this emerging field.