Recent advances in the synthesis, especially in the area of crystal growth, of a new family of oxides structurally related to the 2H-hexagonal perovskite are presented. This family of oxides, whose structures consist of chains of alternating octahedra and trigonal prisms along the c-direction, can be described by the general formula A3n+3mAn′B3m+nO9m+6n. An introduction to this structural description, which allows for a continuum of structures with an increasing ratio of octahedra to trigonal prisms, is given; in essence, this can lead to a never-ending group of structurally diverse members. Instrumental in the understanding of these structures has been the application of the superspace group formalism, which led to the successful determination of the structures of a growing number of these oxides, both commensurate and incommensurate; its usefulness to the structural characterization of these phases is discussed. The combination of the structural description, including the superspace group formalism, and the synthesis techniques have enabled this field to expand. Examples from nearly every section of the periodic table are provided to illustrate both synthetic challenges and the existence of different structural polytypes.