Nanoscale metal oxide memristors have potential in the development of brain-inspired computing systems that are scalable and efficient. In such systems, memristors represent the native electronic analogues of the biological synapses. In this work, we show cerium oxide based bilayer memristors that are forming-free, low-voltage (∼|0.8 V|), energy-efficient (full on/off switching at ∼8 pJ with 20 ns pulses, intermediate states switching at ∼fJ), and reliable. Furthermore, pulse measurements reveal the analog nature of the memristive device; that is, it can directly be programmed to intermediate resistance states. Leveraging this finding, we demonstrate spike-timing-dependent plasticity, a spike-based Hebbian learning rule. In those experiments, the memristor exhibits a marked change in the normalized synaptic strength (〉30 times), when the pre- and post-synaptic neural spikes overlap. This demonstration is an important step towards the physical construction of high density and high connectivity neural networks.