What can we learn from modifing gravity ?

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I will review models of modified gravity in the infrared and show how extra degrees of freedom present in these theories get screened via the Vainshtein mechanism. That mechanism comes hand in hand with its own share of peculiarities: classical superluminalities, strong coupling and perturbative non-analyticity of the S-matrix to name a few. From a traditional effective field viewpoint such effects are disastrous but I will present the first hints in understanding these theories beyond the traditional perspective and their implications not only for gravity but also for our understanding of a certain class of field theories.