In addition to its therapeutic benefits, minimally invasive surgery offers the potential for video recording of the operation. The videos may be archived and used later for reasons such as cognitive training, skills assessment, and workflow analysis. Methods from the major field of video content analysis and representation are increasingly applied in the surgical domain. In this paper, we review recent developments and analyze future directions in the field of content-based video analysis of surgical operations. The review was obtained from PubMed and Google Scholar search on combinations of the following keywords: 'surgery', 'video', 'phase', 'task', 'skills', 'event', 'shot', 'analysis', 'retrieval', 'detection', 'classification', and 'recognition'. The collected articles were categorized and reviewed based on the technical goal sought, type of surgery performed, and structure of the operation. A total of 81 articles were included. The publication activity is constantly increasing; more than 50% of these articles were published in the last 3 years. Significant research has been performed for video task detection and retrieval in eye surgery. In endoscopic surgery, the research activity is more diverse: gesture/task classification, skills assessment, tool type recognition, shot/event detection and retrieval. Recent works employ deep neural networks for phase and tool recognition as well as shot detection. Content-based video analysis of surgical operations is a rapidly expanding field. Several future prospects for research exist including, inter alia, shot boundary detection, keyframe extraction, video summarization, pattern discovery, and video annotation. The development of publicly available benchmark datasets to evaluate and compare task-specific algorithms is essential.