Zinc-blende and wurtzite are the most common structures for binary compound semiconductors. Aluminum nitrides (AIN), one of the most promising materials for deep ultraviolet light-emitting diodes, have a wurtzite structure as an equilibrium phase due to its strong ionicity. Silicon carbide (SiC) is widely used as a substrate for heteroepitaxial growth of AlN, since SiC has a hexagonal structure whose lattice constant is close to that of AIN. Different from other compound semiconductors, SiC can have many different crystalline structures, called polytypism. Among various polytypes of SiC, large-size high-quality wafers are available for 4H and 6H structures. When AlN is grown on a 4H- or 6H-SiC basal plane (0001), normal, wurtzite-structured AIN is obtained. On the other hand, when AlN is grown on a nonbasal SiC plane, such as nonpolar (1100) or (1120), what is expected? If ideal growth is realized, AIN will follow the crystalline structure of SiC (i.e., the polytype of the SiC substrate will be replicated to the AIN epitaxial layer). Nonpolar nitride growth has attracted much attention to eliminate undesirable internal electric fields due to the polarization in nitride heterostructures. In addition, nonpolar nitride growth on SiC also allows an opportunity to obtain nitrides with new crystalline structures. In this article, the polytype replication growth of AIN on nonpolar SiC substrates is reviewed.