Modelling functionalities of the brain in human-robot interaction contexts requires a real-time understanding of how each part of a robot (motors, sensors, emotions, etc.) works and how they interact all together to accomplish complex behavioural tasks while interacting with the environment. Human brains are very efficient as they process the information using event-based impulses also known as spikes, which make living creatures very efficient and able to outperform current mainstream robotic systems in almost every task that requires real-time interaction. In recent years, combined efforts by neuroscientists, biologists, computer scientists and engineers make it possible to design biologically realistic hardware and models that can endow the robots with the required human-like processing capability based on neuromorphic computing and Spiking Neural Network (SNN). However, while some attempts have been made, a comprehensive combination of neuromorphic computing and robotics is still missing. In this article, we present a systematic review of neuromorphic computing applications for socially interactive robotics. We first introduce the basic principles, models and architectures of neuromorphic computation. The remaining articles are classified according to the applications they focus on. Finally, we identify the potential research topics for fully integrated socially interactive neuromorphic robots.