The shift to online instruction around the world has been hastened due to COVID-19 and in response to challenges of maintaining the integrity of remote assessments. Browser-based proctoring systems powered by AI have become popular means of detecting tab switching, screen splitting, and other potential misconduct through real-time browser monitoring and periodic webcam monitoring. Proctoring tools allow exams to be more secure and offer some level of flexibility for schools and learners alike. However, concerns continue to persist regarding data privacy, algorithmic bias, and the accuracy of technical readings. Systems often cannot achieve reliability and fairness and also integrate with Learning Management Systems (LMS). This survey describes current AI-based remote proctoring systems in post-secondary education, and considers their methods, limitation, and ethical implications. A hybrid human-in-the-loop framework, that combines assistance of automated monitoring with human judgment, is suggested below to narrow detection capabilities, reduce bias, and improve transparency of digital examination.