In this chapter, the sub-grid closure models for the LES methodology are presented. In Sect. 9.1, an introduction to this topic is presented. In Sect. 9.2, the general outline of this family of closure models is presented. The Smagorinsky sub-grid model is presented in Sect. 9.3. In Sect. 9.4, the relationship between the Smagorinsky model and the Prandtl mixing length model is presented. The sub-grid model of the second-order structure function of velocity is described in Sect. 9.5. Germano's dynamic sub-grid modeling is presented in Sect. 9.6. Sub-grid modeling for irregular or nonuniform meshes is presented. In Sect. 9.8, considerations regarding post-processing of results are presented. In Sect. 9.9, considerations are presented regarding the cutting wave number. Considerations of numerical methods for LES are presented in Sect. 9.10. In Sect. 9.11, an analysis of mesh refinement for LES is presented. Illustrative results for LES are presented in Sect. 9.12. An example of computational experimentation in fluid dynamics is presented in Sect. 9.13. In Sect. 9.14, the fundamentals for hybrid turbulence closure models are presented. This chapter ends with a list of exercises.