Approximable triangulated categories, as introduced and developed by Neeman, provide a solid framework for studying localization sequences within triangulated categories. In this talk, we demonstrate that a recollement of approximable triangulated categories induces interesting short exact sequences of both triangulated subcategories and Verdier quotient categories. Additionally, we discuss applications of these results within the derived categories of finite-dimensional algebras, DG algebras, and schemes. This is based on joint work with Yongliang Sun.