Efforts to develop scalable learning algorithms for implementation of networks of spiking neurons in silicon have been hindered by the considerable footprints of learning circuits, which grow as the number of synapses increases. Recent developments in nanotechnologies provide an extremely compact device with low-power consumption.In particular, nanoscale resistive switching devices (resistive random-access memory (RRAM)) are regarded as a promising solution for implementation of biological synapses due to their nanoscale dimensions, capacity to store multiple bits and the low energy required to operate distinct states. In this paper, we report the fabrication, modeling and implementation of nanoscale RRAM with multi-level storage capability for an electronic synapse device. In addition, we first experimentally demonstrate the learning capabilities and predictable performance by a neuromorphic circuit composed of a nanoscale 1 kbit RRAM cross-point array of synapses and complementary metal-oxide-semiconductor neuron circuits. These developments open up possibilities for the development of ubiquitous ultra-dense, ultra-low-power cognitive computers.