The Josephson effects are basic properties of superconducting junctions, which demonstrate the macroscopic quantum aspect of superconductivity and have at the same time numerous applications. The underlying transport processes and - especially the fluctuations of the current - are not fully understood. In view of current utilizations of Josephson contacts in technologically relevant current standards and advanced concept like quantum information processing, this situation needs to be improved. Our goal is to develop in collaboration with Czech partners a novel theoretical approach to the transport of charge in superconducting junctions using Keldysh Green's functions, which allows to treat Coulomb interaction and the coupling to the electromagnetic environment on the same footing. We demonstrate our method in several examples, ranging from diffusive normal metal, two-dimensional quasi-relativistic graphene to quantum dots. By comparing stochastic methods with a microscopic quantum mechanical treatment, we aim at a better understanding of the resistive transition of superconducting junctions, which is not only the limiting factor on the current quantization, but also instrumental for the use in quantum processing.