Understanding the glass and jamming transitions is a long standing challenge which is of interest to several fields from statistical mechanics and soft matter, to material sciences and biophysics. \par Are glasses more than just liquids which have become so viscous that they cannot flow anymore? Is the dramatic slowing down of their dynamics related to a true underlying phase transition? \par Recent experimental results, triggered by new theoretical ideas, have shown direct evidence that dynamical correlations increase lowering the temperature, thus giving strong support to a positive answer to both questions. Furthermore, quantitative and qualitative theoretical predictions on dynamical correlations have started to be tested and are helping to prune down different theories which have remained up to now difficult to confirm or to falsify for lack of precise, testable predictions. In this talk I shall discuss these new results focusing in particular on our theoretical findings and their comparison to experiments.