Polymeric graphitic carbon nitride materials (for simplicity: g-C3N4) have attracted much attention in recent years because of their similarity to graphene. They are composed of C, N, and some minor H content only. In contrast to graphenes, g-C3N4 is a medium-bandgap semiconductor and in that role an effective photocatalyst and chemical catalyst for a broad variety of reactions. In this Review, we describe the “polymer chemistry” of this structure, how band positions and bandgap can be varied by doping and copolymerization, and how the organic solid can be textured to make it an effective heterogenous catalyst. g-C3N4 and its modifications have a high thermal and chemical stability and can catalyze a number of “dream reactions”, such as photochemical splitting of water, mild and selective oxidation reactions, and—as a coactive catalytic support—superactive hydrogenation reactions. As carbon nitride is metal-free as such, it also tolerates functional groups and is therefore suited for multipurpose applications in biomass conversion and sustainable chemistry.