This paper discusses numerical and modeling issues that arise in cell-centered finite-volume methods (FVM) for large eddy simulation (LES) of compressible flows on unstructured grids. These are: accuracy and stability of flux interpolation scheme, shock capturing strategy, and subgrid-scale (SGS) modeling. To enhance the accuracy of flux reconstruction, a new scheme with added first derivative term from each cell center is proposed, and tested for various benchmark problems. It is shown that stability as well as accuracy is determined by the formulation of gradient at cell center. As a shock-capturing method, a characteristic based filter is formulated for cell-centered FVM on unstructured grids. The filter is combined with a sensor based on the local divergence and vorticity. Also, a one-equation subgrid model based on the subgrid kinetic energy transport equation for compressible flows is proposed.