I will discuss a link between Hall algebras and the localization of categories. From a hereditary exact model category $\mathcal{M}$ satisfying certain finiteness conditions, we construct a unital associative "semi-derived Hall algebra". We show that it is a free module over a twisted group algebra of a certain quotient of Grothendieck group $K_0(\mathcal{W})$ of the full subcategory of $w$-trivial objects, with a basis parametrized by the isomorphism classes of objects in the (triangulated) homotopy category $\mbox{Ho}(\mathcal{M})$. We prove that it is isomorphic to an appropriately twisted tensor product of this group algebra with the derived Hall algebra of $\mbox{Ho}(\mathcal{M})$, when both of them are well-defined. The twisted group algebra of $K_0(\mathcal{W})$ plays the role of the quantum torus of "coefficients", as in the construction of quantum cluster algebras. In a similar way, we associate Hall-like algebras to localization pairs of triangulated differential graded categories. I will discuss their relation to graded quiver varieties and to categorification of modified quantum groups.