Resistive random access memory (RRAM) technologies, often referred to as memristors, hold fantastic promise for implementing novel in-memory computing systems for massively parallel, low-power and low-latency computation. Compared to conventional systems, these solutions offer promising advantages in terms of energy efficiency and computing power when processing AI workloads. This talk will first present the role of RRAM to enable the hardware implementation of Spiking Neural Networks (SNN). Second, we will present a new path towards realizing intelligent systems, compatible with fundamental resistive memory properties, particularly cycle-to-cycle variability, to bring learning to the edge.