Long implicated in aversive processing, the amygdala is now recognized as a key component of the brain systems that process rewards. Beyond reward valuation, recent findings from single-neuron recordings in monkeys indicate that primate amygdala neurons also play an important role in decision-making. The reward value signals encoded by amygdala neurons constitute suitable inputs to economic decision processes by being sensitive to reward contingency, relative reward quantity and temporal reward structure. During reward-based decisions, individual amygdala neurons encode both the value inputs and corresponding choice outputs of economic decision processes. The presence of such value-to-choice transitions in single amygdala neurons, together with other well-defined signatures of decision computation, indicate that a decision mechanism may be implemented locally within the primate amygdala. During social observation, specific amygdala neurons spontaneously encode these decision signatures to predict the choices of social partners, suggesting neural simulation of the partner's decision-making. The activity of these 'simulation neurons' could arise naturally from convergence between value neurons and social, self-other discriminating neurons. These findings identify single-neuron building blocks and computational architectures for decision-making and social behavior in the primate amygdala. An emerging understanding of the decision function of primate amygdala neurons can help identify potential vulnerabilities for amygdala dysfunction in human conditions afflicting social cognition and mental health.