This Special Issue of the IEEE Journal on Emerging and Selected Topics in Circuits and Systems (JETCAS) is devoted to showcase the latest research achievements on memristive circuits and systems with special focus on edge-computing applications. Over the past few years, the field of circuits and systems has witnessed significant changes, which have inevitably accompanied the progressive approach of the CMOS technology aggressive downscaling trend to an unavoidable end, given the clear impossibility to reduce the transistor dimensions below the atomic scale, in the near future. Tremendous efforts are being made in search for novel devices and circuits toward the development of disruptive nanotechnologies, enabling the fabrication of multi-purpose devices and circuits, which would allow to foster sustainable progress in integrated circuit design, despite further shrinking in transistor sizes shall no longer be feasible soon. In this regard, memristors, exhibiting the extraordinary capability to combine, within a single miniaturized 3-D space, data sensing, processing, and storage functionalities, offer a plethora of novel opportunities for integrated circuit design, paving the way toward the conception of multi-purpose CMOS-compatible nano-circuits, which are bound to improve the performance of state-of-theart computing machines.