The synaptic networks in the amygdala have been the subject of intense interest in recent times, primarily because of the role of this structure in emotion. Fear and its extinction depend on the workings of these networks, with particular interest in extinction because of its potential to ameliorate adverse symptoms associated with post-traumatic stress disorder. Here we place emphasis on the extinction networks revealed by recent techniques, and on the probable plasticity properties of their synaptic connections. We use modules of neurons representing each of the principal components identified as involved in extinction. Each of these modules consists of neural networks, containing specific ratios of excitatory and specialized inhibitory neurons as well as synaptic plasticity mechanisms appropriate for the component of the amygdala they represent. While these models can produce dynamic output, here we concentrate on the equilibrium outputs and do not model the details of the plasticity mechanisms. Pavlovian fear conditioning generates a fear memory in the lateral amygdala module that leads to activation of neurons in the basal nucleus fear module but not in the basal nucleus extinction module. Extinction protocols excite infralimbic medial prefrontal cortex neurons (IL) which in turn excite so-called extinction neurons in the amygdala, leading to the release of endocannabinoids from them and an increase in efficacy of synapses formed by lateral amygdala neurons on them. The model simulations show how such a mechanism could explain experimental observations involving the role of IL as well as endocannabinoids in different temporal phases of extinction.