Testing a non-minimal coupling between matter and curvature and beyond

Abstract: One of the most interesting and current phenomenological extensions of General Relativity is the so-called f(R) class of theories; a natural generalization of this includes an explicit non-minimal coupling between matter and curvature. In this talk, I review the main characteristics of this model, as well as its applicability and compatibility with observables in a wide range of contexts --- including astrophysics, dark matter, cosmology and inflation.