Bearing these ideas in mind, in this special issue, we intend to stimulate the attention of the research community, in general, and of the readers of the Journal of Computational and Nonlinear Dynamics, in particular. In recent years, the powerful computational methods and the analysis of nonlinear phenomena have led to the emergence of discontinuous dynamical systems and of fractional dynamical systems. Such phenomena can be observed almost everywhere. In order to enrich the spectrum of the special issue, the selected articles cover the theoretical and applied studies in discontinuous and fractional dynamical systems from physics and engineering. Therefore, this special issue includes 18 articles spanning through mathematical theory, modeling, implementation, and control. Many readers may feel “uncomfortable” for what is achieved by this special issue, and they may decide to revisit the latest research results in these promising areas. If this is a case, then this special issue has served its purpose.