In joint work with Daniel Litt, we define a "canonical path" between any two points of a smooth connected complex variety X so that iterated integrals of 1-forms on X along the "canonical path" are single-valued (unlike iterated integrals along genuine paths). We show that many interesting examples of single-valued functions arise from this formalism. The talk will be self-contained and will discuss the theory of iterated integrals, why we care about them, and the mixed Hodge theory that governs them.