The neuronal systems that promote protective defensive behaviours have been studied extensively using Pavlovian conditioning. In this paradigm, an initially neutral-conditioned stimulus is paired with an aversive unconditioned stimulus leading the subjects to display behavioural signs of fear. Decades of research into the neural bases of this simple behavioural paradigm uncovered that the amygdala, a complex structure comprised of several interconnected nuclei, is an essential part of the neural circuits required for the acquisition, consolidation and expression of fear memory. However, emerging evidence from the confluence of electrophysiological, tract tracing, imaging, molecular, optogenetic and chemogenetic methodologies, reveals that fear learning is mediated by multiple connections between several amygdala nuclei and their distributed targets, dynamical changes in plasticity in local circuit elements as well as neuromodulatory mechanisms that promote synaptic plasticity. To uncover these complex relations and analyse multi-modal data sets acquired from these studies, we argue that biologically realistic computational modelling, in conjunction with experiments, offers an opportunity to advance our understanding of the neural circuit mechanisms of fear learning and to address how their dysfunction may lead to maladaptive fear responses in mental disorders.