Abstract: We study the embedded deformations of a smooth coisotropic submanifold of a holomorphic Poisson manifold, by describing the controlling DGLA and the relation with the homotopy Lie algebroid of Cattaneo et al. Moreover we show that if the Hodge to de Rham spectral sequence of the submanifold degenerate at E_1, then every first order deformation induced by the anchor map is unobstructed (joint work with R. Bandiera).