Evolutionary-related protein sequences have been selected to preserve a common function and fold. Residues in contact in this conserved structure are coupled by evolution and show correlated mutational patterns. The exponential growth of sequenced genomes makes it possible to detect these coevolutionary coupled pairs and to infer three-dimensional folds from predicted contacts. But how far can we push the prediction of native folds? Can we predict the conformational heterogeneity of a protein directly from sequences? We address these questions developing an accurate contact prediction algorithm and a protein coarse-grained model, and exploring conformational landscapes congruent with coevolution. We find that both structural and dynamical properties can be already recovered using evolutionary information only.