Exactly unsolved problems of interacting 1D fermions

Applications of the integrable system techniques to the non-equilibrium transport problems are discussed. We describe one-dimensional electrons tunneling through a point-like defect either by the s-d exchange (Kondo) mechanism, or via the resonanse level (Anderson) mechanism. These models are potential candidates to be solved exactly in the presence of arbitrary external bias. We draw attention also to several mesoscopical systems which can be tackled by the massless form-factor approach, as perturbations of integrable models. The basic unperturbed model is the massless sine-Gordon model with the interaction (cosine) term restricted to one point, which is integrable. It is being perturbed by the second interaction term, which destroys integrability. Quasi-exact results can be obtained by making use of the basis of massless quasiparticles of the sine-Gordon model.