I will give an overview of a class of non-local infrared modifications of general relativity which perform remarkably well when compared with data and have the same number of parameters as LCDM. After clarifying some subtleties related to the use of non-localities, I’ll concentrate on the application to cosmology, pointing out some general yet powerful criteria to assess the viability of a model. I’ll conclude with some recent results on possible extensions of the models already known.