Nonequilibrium Dynamics of Fluctuating Lines

These notes are for the proceedings of the NATO Advanced Study Insitutue on "Scale Invariance, Interfaces, and Non--Equilibrium Dynamics", held at the Isaac Newton Institute, 20--30 June 1994. The four lectures address a number of issues related to dynamic fluctuations of lines in non-equilibrium circumstances. The first two are devoted to the critical behavior of contact lines and flux lines depinning from impurities. It is emphasized that anisotropies in the medium lead to different universality classes. The importance of nonlinearities for moving lines are discussed in the context of flux lines and polymers in the last two lectures. A dynamic form birefringence is predicted for drifting polymers.