There is a deeply entrenched view in philosophy and physics according to which closed, i.e., isolated, systems are conceived of as fundamental. This is the closed systems view. On the closed systems view, when a system, S, is actually open, i.e., when it is actively being influenced by its environment, this is described in terms of a dynamical coupling between it and a separate system E such that S and E together form an isolated system. We argue against this view, and in favor of the alternative open systems view. Open systems, i.e., systems in interaction with their environment, are conceived of as fundamental on the open systems view, and the influence of the environment on S is not represented in terms of a separate system but rather via the dynamical equations that govern S's evolution. Taking quantum theory as our case study, we argue in particular that what we call the general quantum theory of open systems (GT), a theoretical framework formulated from the open systems point of view that describes the dynamics of systems in terms of linear maps on density operators, is both conceptually wider and more fundamental than standard quantum theory (ST), formulated from the closed systems point of view. Specifically, we consider orthodox (neo-Copenhagen, pragmatist, QBist, relational, etc.) and Everettian interpretations of ST, as well as hidden-variables interpretations, and show that there are reasons to take GT to be more fundamental than ST on each.