  We study transport properties of quantum impurity systems using the
functional renormalization group. The latter is an RG-based diagrammatic tool
to treat Coulomb interactions in a fast and flexible way. Prior applications,
which employed a simple first-order (Hartree-Fock-like) scheme to truncate the
FRG flow equations within the Matsubara formalism, succeeded in accurately
describing linear transport of various quantum dot geometries at zero
temperature T=0. In a nutshell, advance in this Thesis is three-fold. First, we
introduce a frequency-dependent second-order approximation in order to
eventually compute finite-energy properties such as the conductance at T>0
(mainly focusing on the single impurity Anderson model). Second, a
generalisation of the Hartree-Fock-like approach to Keldysh space allows for
addressing the non-equilibrium steady-state dynamics of the interacting
resonant level model. Third, we investigate the physics of a quantum dot
Josephson junction as well as the charging of a single narrow level using the
first-order scheme.
