A scaling and similarity technique is a useful tool for developing and testing reduced models of complex phenomena, including plasma phenomena. In this paper, similarity and scaling arguments will be applied to highly dynamical systems where the plasma is evolving from some initial to some final state, which may differ dramatically from each other in size and plasma parameters. A question then arises whether, in order to better understand the behavior of one such system, is it possible to create another system, possibly much smaller (or larger) than the original one, but whose evolution would accurately replicate that of the original one, from its initial to its final state. This would allow a researcher, by an experimental study of this second system, to make confident predictions about the behavior of the first one (which may be otherwise inaccessible, as is the case of some astrophysical objects, or too expensive and hard to diagnose, as in the case of fusion applications of pulsed plasma systems, or for other reasons). The scaling and similarity techniques for dynamical plasma systems will be presented as a set of case studies of problems from various domains of plasma physics, including collisional and collisionless plasmas. Among the results discussed are similar for MHD systems with an emphasis on high-energy-density laboratory astrophysics, interference between collisionless and collisional phenomena in the context of shock physics, and similarity for liner-imploded plasmas.