Digital technologies in the modern era are almost mandatory for the presentation of all types of cultural heritage. Virtual depictions of crafts and traditions offer the users the possibility of time travel, taking them to the past through the use of 3D reconstructions of cultural monuments and sites. However, digital resources alone are not enough to adequately present cultural heritage. Additional information on the historical context in the form of stories, virtual reconstructions, and digitized objects is needed. All of this can be implemented using a digital multimedia presentation technique called digital storytelling. Nowadays, an integral part of many museum exhibitions is interactive digital storytelling. This paper gives an overview of the techniques and discusses different means of facilitating interaction on digital storytelling applications for virtual cultural heritage presentations. We describe the ways in which natural interaction and interaction via eXtended Reality (Virtual and Augmented Reality) applications for cultural heritage are made possible. Users will find the stories told through these applications educational and entertaining at the same time. Through user-experience studies, we measure the user edutainment level and present how users react to implemented interactions.