IT departments of organisations go to great lengths to protect their IT infrastructure from external attackers. However, internal attacks also pose a large threat to organisations. Despite detection and prevention of insider attacks being an active field of research, so far such techniques are rarely being deployed in practice. This paper outlines the state of the art in the field and identifies open research problems in the area. The lack of unified definitions and publicly available datasets for evaluation is detrimental to the comparability of published results in the field and hinders the continual improvement of technology. Another important problem is that of data protection: On the one hand, the data captured for insider attack detection could also be used for surveillance of employees, so it should be anonymised. On the other hand, anonymisation may make some attacks undetectable, leading to a trade-off between detectability of attacks and privacy.