This review article focuses on recent advances and challenges in the field of thermotropic cubic phases of the bicontinuous type (Cub bi ) formed by low molecular mass molecules. In the Cub bi phases, the constituent molecules self-organize into 3D network structures, although local molecular diffusional motions are preserved to some extent. This review illustrates which types of molecules form such structures, and summarizes the latest developments in structural characterization. Moreover, their phase behaviors, and analogies and differences in comparison with other related systems such as lyotropic liquid crystals and block copolymers are discussed. Finally, potential applications utilizing the dynamically ordered 3D network structures are presented.