While the model theory of locally compact fields are well understood (starting from pioneering decidability works of Tarski and Ax-Kochen), very little is known regarding the model theory of number fields due to their Godelian undecidability where a direct approach is not possible. In this talk, I will give some model-theoretic results for number fields that are established from local theories. Such a local to global transition is made via motivic and $p$-adic integration to establish a result on meromorphic continuation of Dirichlet series that are Euler products of local integrals defined by means of model-theoretic data, and to understand model theory and measure theory of adeles. This result will then give solution to a number of open problems in number theory and algebra.