The so-called “concordance” cosmological model has been the cornerstone of observational cosmology. Even if it is based on components of unknown physical origin (inflation, dark matter, the cosmological constant) its agreement with an impressive set of independent observational measurements made it quite successful for many years. However, recently several new observations posed a serious challenge to this model: a more than 4 sigma difference between the measured value of the Hubble constant and its predicted value based on CMB data, a deviation between the observed and predicted expansion of the Universe at high redshift, and a tension between the most recent Planck CMB data and the hypothesis of flatness. I will review the main observational data supporting the standard scenario, and I will discuss these recent tensions, and possible solutions beyond the “concordance” model.