In the last fifteen years we have witnessed to an impetuous advancement in the theory of nonequilibrium fluctuations, triggered by the discovery of a number of relations, collectively known as Fluctuation Theorems, which link the full nonlinear response to equilibrium thermodynamic properties. Experimental investigations of these exact relations in the quantum regime is yet in its infancy, while we are currently witnessing a growing interest into these relations by the experimental condensed matter and quantum information communities. In an effort to stay at the forefront of new developments, this project aims at proposing feasible experiments where quantum fluctuation relations can be verified and applied. This will be achieved by pursuing two objectives, the first concerns the verification of fluctuation relations, the second their application. In both cases we will focus on experimental set-ups involving solid state superconducting devices. These are very promising tools for the development of future quantum technologies. Our first objective is to develop concrete and feasible proposals for circuit QED experiments aimed at measuring the work statistics and verifying the fluctuation relations in the quantum domain. Our second objective is to use fluctuation relations as a tool for improving the thermodynamic efficiency of solid state devices. In particular we will focus on a device, the Cooper pair pump, which hold a promise for geometric quantum computation.