abstract: In the first of the two talks I shall explain the notion of generalized Calabi-Yau structures, a notion introduced by Hitchin, in the case of K3 surface and explain the global geometry of their moduli space. These structures give rise to new weight-two Hodge structures on the cohomology of a K3 surface and are related to Brauer classes, B-fields etc. In the second talk I will report on a joint work with P. Stellari on derived categories of generalized K3 surfaces. The talks will be based on the two eprints Equivalences of twisted K3 surfaces (http:/it.arxiv.orgabsmath.AG0409030) Generalized Calabi-Yau structures, K3 surfaces, and B-fields (http:/it.arxiv.orgabsmath.AG0306162)