Intangible cultural heritage (ICH) as a field of research and site for digital efforts has grown significantly since the UNESCO 2003 Convention for the Safeguarding of Intangible Heritage. In contrast to tangible heritage, where cultural identities are manifested through physical objects, intangible cultural expressions are defined through tacit reliances and embodied practices. Such practices are usually bodily communicated, enacted, socially transmitted, and constantly evolving. Burgeoning trends in computational heritage and ICT applications have played a crucial role in safeguarding ICH as they produce versatile resources while making them accessible to the public. Nevertheless, most of the inventions are object-centric and cater to conserving material-based knowledge bases. Few endeavors thus far have fully supported the recording, representing, and reviving of the living nature of ICH. One of the challenges now faced is to find appropriate forms, together with efficient methods, to document the ephemeral aspects of intangible heritage. Another barrier is to find effective ways to communicate the knowledge inextricably linked to people. In response, recent efforts have embarked on capturing the “live” and “active” facets of the embodied cultures, which entails addressing technological and curatorial complexity to communicate the material and immaterial aspects within a meaningful context. Meanwhile, advancements in experimental museology have opened up new modes of experiential narratives, particularly through visualization, augmentation, participation, and immersive embodiment. Novel practices of cultural data computation and data sculpting have also emerged toward the ideal of knowledge reconstruction. This article outlines state-of-the-art models, projects, and technical practices that have advanced the digitization lifecycle for ICH resources. The review focuses on several critical but less studied tasks within digital archiving, computational encoding, conceptual representation, and interactive engagement with the intangible cultural elements. We aim to identify the advancements and gaps in the existing conventions, and to envision opportunities for transmitting embodied knowledge in intangible heritage.