We discuss a non-local infrared modification of gravity recently proposed by our group. The model has the same number of parameters as $\Lambda$CDM, with a mass scale $m$ replacing the cosmological constant, and is very successful phenomenologically. It generates dynamically a dark energy and its cosmological perturbations are well behaved. Implementing its cosmological perturbations in a Boltzmann code we find that it fits CMB, SNe, BAO and structure formation data remarkably well, with an overall $\chi^2$ competitive with $\Lambda$CDM. We will discuss directions of investigations for understanding how such an effective non-local theory could emerge from a fundamental local QFT.