  Reduced order models (ROMs) have achieved a lot of success in reducing the
computational cost of traditional numerical methods across many disciplines.
For convection-dominated (e.g., turbulent) flows, however, standard ROMs
generally yield inaccurate results, usually affected by spurious oscillations.
Thus, ROMs are usually equipped with numerical stabilization or closure models
to account for the effect of the discarded modes. The literature on ROM
closures and stabilizations is large and growing fast. In this paper, we focus
on one particular type of ROM closures and stabilizations that are inspired by
Large Eddy Simulation (LES). These ROMs, which we call LES-ROMs, are extremely
easy to implement, very efficient, and accurate. Carefully tuned LES-ROMs can
accurately capture the average physical quantities of interest in challenging
convection-dominated flows in many applications. LES-ROM are constructed by
leveraging spatial filtering, i.e., the same principle used to build classical
LES models. This ensures a modeling consistency between LES-ROMs and the
approaches that generated the data used to train them. It also ``bridges'' two
distinct research fields (LES and ROMs), disconnected until now. This paper is
a review of LES-ROMs. It starts with a description of a versatile LES strategy
called evolve-filter-relax (EFR) that has been successfully used as a full
order method. We then show how the EFR strategy, and spatial filtering in
general, can be leveraged to construct LES-ROMs. Several applications of
LES-ROMs are presented. Finally, we draw conclusions and outline several
research directions and open questions in the LES-ROM development. While we do
not claim this review to be comprehensive, we certainly hope it serves as a
brief and friendly introduction to this exciting research area, which has a lot
of potential in practical numerical simulation of convection-dominated flows.
