Carbon nitride compounds with high N : C ratios and graphitic to polymeric structures are being investigated as potential next-generation materials for incorporation in devices for energy conversion and storage as well as for optoelectronic and catalysis applications. The materials are built from C- and N-containing heterocycles with heptazine or triazine rings linked via sp2-bonded N atoms (N(C)3 units) or -NH- groups. The electronic, chemical and optical functionalities are determined by the nature of the local to extended structures as well as the chemical composition of the materials. Because of their typically amorphous to nanocrystalline nature and variable composition, significant challenges remain to fully assess and calibrate the structure-functionality relationships among carbon nitride materials. It is also important to devise a useful and consistent approach to naming the different classes of carbon nitride compounds that accurately describes their chemical and structural characteristics related to their functional performance. Here we evaluate the current state of understanding to highlight key issues in these areas and point out new directions in their development as advanced technological materials.