In recent years, data-driven stories have found a firm footing in journalism, business, and education. They leverage visualization and storytelling to convey information to broader audiences. Likewise, immersive technologies, like augmented and virtual reality devices, provide excellent potential for exploring and explaining data, thus inviting research on how data-driven storytelling transfers to immersive environments. To gain a better understanding of this exciting novel research area, we conducted a scoping review on the emerging notion of immersive data-driven storytelling, extended by surveying immersive data journalism and by analyzing immersive games, selected based on community reviews and tags. We present our methodology for the survey and discuss prominent themes that coalesce the knowledge we extracted from the literature, journalism, and games. These themes include, among others, the spatial embodiment of narration, the incorporation of the users and their context into narratives, and the balance between guiding the user versus promoting serendipity. Our discussion of these themes reveals research opportunities and challenges that will inform the design of immersive data-driven stories in the future.