The brain is the most important part of any living creature. It acts according to the changing environment. The brain performs computations in parallel as it has neurons which are electrically active cells that operate simultaneously. Neurons influence other’s activity via synapses. Neurons and synapses form the network. This paper presents a review of neuron models that try to emulate the real neurons and the synaptic plasticity rule which govern the synaptic weights. The neuron circuits based on the integrate and fire model and Izhikevich model are presented which are implemented in 0.18mm technology in cadence virtuoso. The plasticity rules are dependent on the neural activity. These rules consider spike timing, spike rate or both to alter the synapse weight. Protocols applicable to these rules are also presented.