Reynolds stress models and traditional large-eddy simulations are reexamined with a view toward developing a combined methodology for the computation of complex turbulent flows. More specifically, an entirely new approach to time-dependent Reynolds-averaged Navier-Stokes (RANS) computations and very large-eddy simulations (VLES) is presented in which subgrid scale models are proposed that allow a direct numerical simulation (DNS) to go continuously to a RANS computation in the coarse mesh/infinite Reynolds number limit. In between these two limits, we have a large eddy simulation (LES) or VLES, depending on the level of resolution. The Reynolds stress model that is ultimately recovered in the coarse mesh/infinite Reynolds number limit has built in nonequilibrium features that make it suitable for time-dependent RANS. The fundamental technical issues associated with this new approach, which has the capability of bridging the gap between DNS, LES and RANS, are discussed in detail. Illustrative calculations are presented along with a discussion of the future implications of these results for the simulation of the turbulent flows of technological importance.