Abstract: We introduce several novel change of measure inequalities for two families of divergences: f-divergences and \alpha-divergences. We show how the variational representation for f-divergences leads to novel change of measure inequalities. We also present a multiplicative change of measure inequality for \alpha-divergences and a generalized version of Hammersley-Chapman-Robbins inequality. Finally, we present several applications of our change of measure inequalities, including PAC-Bayesian bounds for various classes of losses and non-asymptotic intervals for Monte Carlo estimates.