Cavity Quantum Electrodynamics (CQED) studies the properties of atoms and photons confined in cavities in situations where the coupling of matter with radiation is much stronger than in free space. I will describe CQED experiments in which microwave photons are controlled and manipulated non destructively by Rydberg atoms crossing the cavity one by one. These experiments illustrate fundamental concepts of quantum physics and demonstrate basic operations of quantum information exchange between light and matter. Similar experiments are now carried out in the related field of Circuit QED, in which Rydberg atoms are replaced by artificial atoms made of superconducting circuits. The light-matter interaction is then much stronger than in CQED, leading to a faster dynamics and opening promising perspectives for applications to quantum information.