This chapter provides a fairly systematic analysis of when quantities that are variant under a dynamical symmetry transformation should be regarded as unobservable, or redundant, or unreal; of when models related by a dynamical symmetry transformation represent the same state of affairs; and of when mathematical structure that is variant under a dynamical symmetry transformation should be regarded as surplus. In most of these cases, the answer is ‘it depends’: that is, it depends on the details of the symmetry in question. A central feature of the analysis is that in order to draw any of these conclusions for a dynamical symmetry, it needs to be understood in terms of its possible extensions to other physical systems, in particular to measurement devices.