Most theoretical and experimental efforts in polyelectrolyte science have been aimed at understanding equilibrium properties. The purpose of this chapter is to call attention to the wide array of kinetic phenomena which occur in polyelectrolyte solutions on their way to equilibrium. Such time-dependent processes include dissolution of dry powders, phase separation, aggregation, gelation, and degradation. Because equilibration times in polyelectrolyte solutions can be quite long, polyelectrolyte solutions may often be used and studied, wittingly or not, in non-equilibrium states. After a brief review of some of the equilibrium properties of polyelectrolyte solutions, a few simple ideas and examples are given to illustrate non-equilibrium processes. A larger emphasis is given to the degradation problem, simply because it is the area of time-dependent phenomena where the author and co-workers have so far made the most quantitative headway.