Online proctoring systems are employed to monitor students during exams, safeguarding assessment integrity when in-person observation is not feasible. The systems leverage advanced technologies, including artificial intelligence (AI) and biometrics, to authenticate students and identify potential exam rule violations. However, concerns about data privacy and security, transparency in data processing and decision-making, and the ethical use of online proctoring systems have been raised. Following a surge in adoption during the COVID-19 pandemic, educational institutions are now critically evaluating the use of online proctoring systems. This research, based on a systematic-narrative hybrid literature review of publicly available descriptions of 33 online proctoring systems, highlights significant shortcomings in data privacy and security and the unspecified use of AI technologies, particularly regarding their role in decision-making on exam rule violations. Proprietary solutions dominate and open-source alternatives are not available. The article explains the dangers inherent in those shortcomings and provides educational institutions with criteria and data for the comparison of online proctoring systems, facilitating an informed system selection in line with educational contexts and values. Further, the article outlines how the introduction of open standards could address the significant shortcomings and the dominance of proprietary approaches. A proctoring profile identity standard is to include a variety of biometric and behavioural markers, created and updated across interactions with exam and generic learning technologies, stored securely, owned and controlled by the student. A proctoring flag standard is to provide a transparent basis for capturing data related to potential exam rule violations, to be evaluated for individual students and across cohorts. Key recommendations to the education sector are to demand more transparency from proctoring systems providers and to work together with students towards the goal of assessment integrity.