Morita equivalence is an important equivalence relation in algebra and geometry. The talk will discuss the classification of Morita equivalent star products on Poisson manifolds in terms of their characteristic classes. We will show that the correspondence between star products and formal Poisson structures (resulting from Kontsevich's formality theorem) has a suitable equivariance property which allows us to express Morita equivalence of star products in Poisson geometric terms (as a "B-field transform"). This is based on joint work with V. Dolgushev and S. Waldmann.