In this thesis, the transport properties and relaxation phenomena in 1D interacting
systems are studied. The electrical transport is investigated in Josephson junction (JJ) chains which show
the remarkable phenomenon of a superconductor-insulator transition. These systems also offer
the possibility to examine relaxation phenomena: we consider the decay of excited plasmonic
waves in such devices. In addition to the relaxation of bosonic excitations in JJ chains, we dis-
cuss the relaxation of high-energy fermions in quantum wires.