We discuss opportunities and challenges for making people experience immersion when interacting with visual data stories. Even though visual data stories are an important means for communicating information, the extent to which viewers feel immersed in such stories has so far been hardly explored. In this chapter, we explore the concept of immersion in visual data stories from the viewpoint of related disciplines in which narratives play an important role. We pay special attention to games research, which shares a focus on graphics and interactivity with our context of visual data stories. From this exploration we derive research opportunities and challenges for immersion in visual data stories.