To realize intelligent functions in electronic devices like a human brain, it is important to develop the electronic devices that can imitate biological neurons and synapses (synaptic electronics). In this paper, we review the critical learning mechanisms for synaptic plasticity. Different electronic devices were developed to mimic biological synapses, such as atomic switch, phase change memory, ferroelectric memory, and electric-double-layer transistors. More importantly, several groups have realized the artificial neuromorphic network using multi-gate transistor architecture. The leap from synapse to neuron to neural network, thus, has been systematically realized using thin films and nanomaterials. The emerging synaptic electronics can have a broader applications and brighter future in the next-generation intelligent nano-electronics.