Summary: We consider various inventory, queueing and reliability models where there is apparent complexity due to interacting components or subsystems. In particular, our analysis focuses on a multi-item inventory model with stochastically dependent demands, a queueing network where there are dependent arrival and service processes, or a reliability model with stochastically dependent component lifetimes. We discuss cases where this dependence is induced only by a random environmental process which the system operates in. This process represents the sources of variation that affect all deterministic and stochastic parameters of the model. Thus, not only the parameters of the model are now stochastic processes, but they are all dependent due to the common environment they are all subject to. Our objective is to provide a convincing argument that, under fairly reasonable conditions, the analysis techniques used in these models as well their solutions are not much more complicated than those where there is no environmental variation.