Originally proved by Piatetski-Shapiro and Shafarevich in 1971, the Torelli theorem for K3 surfaces is a deep theorem. Instead of the traditional proof, we present one, following Huybrechts, that is based on the study of the period maps. Using twistor lines, one shows the period map from the moduli space of marked K3 surfaces to the period domain is injective on each connected component. Furthermore, there are at most 2 connected components for the moduli that are switched under -Id, a result following from the study of monodromy groups. Torelli's theorem then follows from the above combined.