Physiological computing uses human physiological data as system inputs in real time. It includes, or significantly overlaps with, brain-computer interfaces, affective computing, adaptive automation, health informatics, and physiological signal based biometrics. Physiological computing increases the communication bandwidth from the user to the computer, but is also subject to various types of adversarial attacks, in which the attacker deliberately manipulates the training and/or test examples to hijack the machine learning algorithm output, leading to possibly user confusion, frustration, injury, or even death. However, the vulnerability of physiological computing systems has not been paid enough attention to, and there does not exist a comprehensive review on adversarial attacks to it. This paper fills this gap, by providing a systematic review on the main research areas of physiological computing, different types of adversarial attacks and their applications to physiological computing, and the corresponding defense strategies. We hope this review will attract more research interests on the vulnerability of physiological computing systems, and more importantly, defense strategies to make them more secure.