The spatial and temporal scales of astrophysical phenomena are typically 10–20 orders of magnitude greater than those of laboratory experiments intended to simulate them. Accordingly, the issue of similarity between the astrophysical phenomenon and its laboratory counterpart becomes quite important. Note also that in astrophysics, one is often dealing with highly dynamical systems, where orders of magnitude variation of the parameters of interest occurs over the duration of an event. In this regard, the similarity problem is more challenging than, say, the familiar problem of establishing a scaling law for the energy confinement time in a steady-state fusion device. We concentrate on astrophysical phenomena which can be reasonably well described by magnetohydrodynamic equations (like, e.g. propagation of the supernova (SN) shock through the progenitor star, and interaction of SN ejecta with an ambient plasma) and formulate a broad class of similarities that can be applied to them. We discuss issues of scalability in situations where the transition to turbulent flows occurs and present the corresponding constraints. We illustrate the general principles by describing several laboratory experiments carried out in a scaled fashion. Discussion of the possibility of scalable experiments directed towards studies of photo-evaporated molecular clouds (thought to be `star nurseries') is presented. An emphasis on the potential role of random magnetic fields is made. A concept of an experiment to generate magnetized jets in Z-pinch devices is presented.