Data-driven computational approaches have evolved to enable extraction of information from medical images with a reliability, accuracy and speed which is already transforming their interpretation and exploitation in clinical practice. While similar benefits are longed for in the field of interventional imaging, this ambition is challenged by a much higher heterogeneity. Clinical workflows within interventional suites and operating theatres are extremely complex and typically rely on poorly integrated intra-operative devices, sensors, and support infrastructures. Taking stock of some of the most exciting developments in machine learning and artificial intelligence for computer assisted interventions, we highlight the crucial need to take context and human factors into account in order to address these challenges. Contextual artificial intelligence for computer assisted intervention, or CAI4CAI, arises as an emerging opportunity feeding into the broader field of surgical data science. Central challenges being addressed in CAI4CAI include how to integrate the ensemble of prior knowledge and instantaneous sensory information from experts, sensors and actuators; how to create and communicate a faithful and actionable shared representation of the surgery among a mixed human-AI actor team; how to design interventional systems and associated cognitive shared control schemes for online uncertainty-aware collaborative decision making ultimately producing more precise and reliable interventions.Index Terms-Artificial intelligence, computer assisted interventions, interventional workflow, intra-operative imaging, surgical planning, data fusion, surgical scene understanding, contextaware user interface, machine and deep learning, surgical data science