Publisher Summary This chapter is concerned with oscillatory phenomena at solid–liquid interface, liquid–liquid interface, solid–liquid and liquid–liquid interface together, liquid–vapor interface, and solid–vapor interface. It discusses both experimental and theoretical studies along with applications. Dynamic instability in complex systems is of considerable current interest in view of its applications in the study of physico-chemical, biological, physiological, geophysical systems, and dynamics of social and economic change including behavioral sciences. Dynamics of weather changes, population, and ecology have also stimulated a good deal of interest. Non-linear phenomena such as temporal oscillations and chemical waves in the case of chemical reactions are governed by the autocatalytic reaction and reaction where the product of autocatalysis is destroyed by some other species. Electro-kinetic phenomena is proved to be useful non-equilibrium phenomena as compared to other phenomena, since the former can be experimentally investigated in the entire non-equilibrium range, from linear to far from equilibrium by controlling the variables. The results can be analyzed using paradigms of non-equilibrium thermodynamics and non-linear dynamics. Besides, such phenomena are also interesting from a physiological angle in connection with the ion transport through nerve cell and rhythmic action potential.