Regular rings -- like Z, Q or a polynomial ring over a field -- are the rings we understand best. In the interest of better understanding the theory of rings and schemes more generally, commutative algebraists and algebraic geometers study singular (non-singular) rings. In particular, we are interested in saying how badly a ring fails to be regular -- because if the failure is not too bad, many powerful techniques developed for regular rings still apply. In this talk, we introduce the Frobenius morphism, a ring map which exists only in prime characteristic. Singularities of this map are called F-singularities, and we discuss several important categories of rings classified by this map -- F-finite, F-split, F-pure, and strongly F-regular rings.