We review modeling techniques for multiresolution three-dimensional scalar fields based on a discretization of the field domain into nested tetrahedral meshes generated through regular simplex bisection. Such meshes are described through hierarchical data structures and their representation is characterized by the modeling primitive used. The primary conceptual distinction among the different approaches proposed in the literature is whether they treat tetrahedra or clusters of tetrahedra, called diamonds, as the modeling primitive. We first focus on representations for the modeling primitive and for nested meshes. Next, we survey the applications of these meshes to modeling multiresolution 3D scalar fields, with an emphasis on interactive visualization. We also consider the relationship of such meshes to octrees. Finally, we discuss directions for further research.