In this talk, we present reduced order models (ROMs) for turbulent flows, which are constructed by using ideas from large eddy simulation (LES) and variational multiscale (VMS) methods.  First, we give a general introduction to reduced order modeling and emphasize the connection to classical Galerkin methods (e.g., the finite element method) and the central role played by data.  Then, we describe the closure problem, which represents one of the main obstacles in the development of ROMs for realistic, turbulent flows. …