While Bayesian methods are extremely popular in statistics and machine\nlearning, their application to massive datasets is often challenging, when\npossible at all. Indeed, the classical MCMC algorithms are prohibitively slow\nwhen both the model dimension and the sample size are large. Variational\nBayesian methods aim at approximating the posterior by a distribution in a\ntractable family. Thus, MCMC are replaced by an optimization algorithm which is\norders of magnitude faster. VB methods have been applied in such\ncomputationally demanding applications as including collaborative filtering,\nimage and video processing, NLP and text processing... However, despite very\nnice results in practice, the theoretical properties of these approximations\nare usually not known. In this paper, we propose a general approach to prove\nthe concentration of variational approximations of fractional posteriors. We\napply our theory to two examples: matrix completion, and Gaussian VB.\n