Recently, Oguiso addressed the following question, attributed to Gizatullin: "Which automorphisms of a smooth quartic K3 surface D in the 3-dimensional projective space are induced by Cremona transformations of the ambient space?'' When D is such a quartic surface, (P^3,D) is an example of a Calabi-Yau pair, that is, a pair (X,D) consisting of a normal projective variety X and an effective Weil divisor D on X such that K_X+D is linearly equivalent to 0. In this talk, I will explain a general framework to study the birational geometry of mildly singular Calabi-Yau pairs. This is joint work with Alessio Corti and Alex Massarenti. Speaker(s): Carolina Araujo (IMPA)