In this paper, we survey techniques for building, encoding and querying Level-Of-Detail (LOD) models of three-dimensional scalar fields based on a domain decomposition into tetrahedral meshes. We focus on continuous LOD models, and we classify them into unstructured (irregular) and regular nested LOD models depending on the mesh subdivision pattern and on the distribution of the data points. Within each class, we review data structures, construction algorithms, as well as techniques for extracting adaptively refined field representations from an LOD model.