I will discuss the relevant statistical tools aimed at testing the concordance of cosmological observations and how they can be used as the most model independent test for the standard cosmological model. These statistical tests are a powerful way of assessing whether a specific model explains the observed measurements or whether there are indications of residual, unaccounted, systematic effects or hints toward new physical phenomena. I will show the results of these tests when applied to state of the art cosmological measurements and discuss the overall level of agreement of the standard cosmological model with observations. I will then move to discuss extensions of the standard model and how these might help in explaining some of the discrepant aspects of observations. In particular I will focus on dark energy and modified gravity models discussing their cosmological phenomenology and highlighting the observational aspects that they improve and that can be used to test them.