Testing gravity with atom interferometry

We developed two types of atom interferometer for gravitational physics experiments: The first is a double Raman interferometer with Rb atoms that we operate as a gravity gradiometer. The second is based on Bloch oscillations of Sr atoms in optical lattices. As in my lectures at the 2013 'E. Fermi' School in Varenna, the aim of these notes is to describe the characteristics of the two interferometers taking as examples the experiments that we performed. I present the schemes of the interferometers, the key steps that allowed us to optimize the setups, their operation and performances. I discuss experiments that we carried out, namely, a precision measurement of the value of the gravitational constant G using the Rb Raman interferometer and the measurement of gravity at small spatial scale using the Sr apparatus, with implications in the search for deviations from Newtonian gravity and as tests of general relativity. I also discuss prospects and possible ideas for future experiments in laboratories on ground and in space.