In this talk, I will survey our group's work to bridge two distinct research fields, large eddy simulation (LES) and reduced order models (ROMs), for efficient and accurate numerical simulations of engineering and geophysical turbulent flows. The models that we have developed, called LES-ROMs, leverage ideas from both LES and ROMs, as well as modern data-driven modeling strategies. The main tool used to construct the new LES-ROMs is explicit spatial filtering, which is employed to model the large spatial structures in the underlying turbulent flow. We have used the new LES-ROMs in the numerical simulation of the turbulent channel flow, which is an extremely challenging test problem for ROMs.