The special case of localization of model categories for simplicial model categories.
A simplicial model category is a presentation of an (infinity,1)-category.
The localization of a simplicial model category accordingly models the localization of the corresponding (infinity,1)-category, i.e. the passage to the a reflective (infinity,1)-subcategory).
A famous example of localizations of simplicial model categories appears in the study of model structures on simplicial presheaves, where it yields a presentation of (infinity,1)-sheafification completely analogous to how ordinary localization described ordinary sheafification:
the global projective/injective model structures on simplicial presheaves on a site $S$ presents the $(\infty,1)$-category of (infinity,1)-presheaves on $S$;
the Bousfield localization of these global model structures at morphisms which are local (stalkwise) weak equivalences yields the local projective/injective model structure on simplicial presheaves on $S$, which then presents the (infinity,1)-category of (infinity,1)-sheaves on $S$.
chapter 9.4 in
section A.3.7 of
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