This talk will address the estimation of predictive densities and their efficiency as measured by frequentist risk. For Kullback-Leibler, α−divergence, L1 and L2 losses, we review several recent findings that bring into play improvements by scale expansion, as well as duality relationships with point estimation and point prediction problems. A range of models is studied and include multivariate normal with both known and unknown covariance structure, scale mixture of normals, Gamma, as well as models with restrictions on the parameter space.