Circuit QED offers the possibility to realizean exceptionally strong coupling between artificial atoms individual superconductingqubits and single microwave photons in a one dimensional waveguide resonator. Thisnew solid state approach to investigate the matter-light interaction on the level of individual quanta also represents a promising hardware architecture for the realization of a scalable quantum information processor. We first summarize and review the important theoretical and experimental principles of this rapidely developing field and give an overview of the relevant literature....