Modified f(R) gravity is a popular and quite general extension of general relativity (GR). The interest for this theory lit up towards the end of the last century, with the perspective that nonlinear corrections to the Einstein-Hilbert action could provide a natural explanation for the accelerated expansion of the universe. At the solar system scales, however, Einstein’s theory is extremely well tested; hence, the high precision, local measurements can place strong constraints on any modified gravity model. In this talk, I address the question of how to build a class of f(R) extensions of GR which are compatible with solar system experiments, without making any preliminary assumption on the properties of f. I reach this aim by perturbatively solving the modified Einstein equations around a Schwarzschild background, and retrieving a posteriori the corresponding f(R). This turns out to be non analytical in R = 0 and should be intended as the leading correction to the Einstein-Hilbert action in the low curvature limit. Furthermore, I show how the parameters characterizing the f(R) class can be set by computing the corrections to four different local observables and comparing with the observations. At larger scales, the resulting model can serve as a constraint for exact f(R)’s working in cosmology, since it provides a correct local limit. 1