The concept of a norm is found widely across fields including artificial intelligence, biology, computer security, cultural studies, economics, law, organizational behaviour and psychology. The concept is studied with different terminology and perspectives, including individual, social, legal and philosophical. If a norm is an expected behaviour in a social setting, then this article considers how it can be determined whether an individual is adhering to this expected behaviour. We call this process monitoring, and again it is a concept known with different terminology in different fields. Monitoring of norms is foundational for processes of accountability, enforcement, regulation and sanctioning. Starting with a broad focus and narrowing to the multi-agent systems literature, this survey addresses four key questions: what is monitoring, what is monitored, who does the monitoring and how the monitoring is accomplished.@en