The development of memristive device technologies has reached a level of maturity to enable the design of complex and large-scale hybrid memristive-CMOS neural processing systems. These systems offer promising solutions for implementing novel in-memory computing architectures for machine learning and data analysis problems. We argue that they are also ideal building blocks for the integration in neuromorphic electronic circuits suitable for ultra-low power brain-inspired sensory processing systems, therefore leading to the innovative solutions for always-on edge-computing and Internet-of-Things (IoT) applications. Here we present a recipe for creating such systems based on design strategies and computing principles inspired by those used in mammalian brains. We enumerate the specifications and properties of memristive devices required to support always-on learning in neuromorphic computing system and to minimize their power consumption. Finally, we discuss in what cases such neuromorphic systems can complement conventional processing ones and highlight the importance of exploiting the physics of both the memristive devices and of the CMOS circuits interfaced to them.Neuromorphic computing has recently received considerable attention as a discipline that can offer promising technological solutions for implementing power-and size-efficient sensory-processing, learning, and Artificial Intelligence (AI) applications 1-5 , especially in cases in which the computing system has to operate autonomously "at the edge", i.e., without having to connect to powerful (but power hungry) server farms in the "cloud". The term "neuromorphic" was originally coined in the early 90's by Carver Mead to refer to mixed signal analog/digital Very Large Scale Integration (VLSI) computing systems based on the organizing principles used by the biological nervous systems 6 . In that context, "neuromorphic engineering" emerged as an interdisciplinary research field deeply rooted in biology that focused on building electronic neural processing systems by exploiting the physics of silicon to directly "emulate" the bio-physics of real neurons and synapses. More recently the definition of the term "neuromorphic" has been extended in two additional directions: on one hand to describe more generic spike-based processing systems engineered to "simulate" spiking neural networks for the exploration of large-scale computational neuroscience models 7-9 ; and on the other hand to describe dedicated electronic neural architectures that make use of both electronic Complementary Metal-Oxide Semiconductor (CMOS) circuits and memristive devices to implement neuron and synapse circuits 10,11 .Another recent and very promising trend in developing dedicated hardware architectures for building accelerated simulators of artificial neural networks is related to the field of machine learning and AI 12,13 . The types of neural networks being proposed within this context are only loosely inspired by biology, are aimed at high accuracy pattern recognition based on large...