A conjecture of Manin predicts an asymptotic formula for the number of rational points of bounded anticanonical height on Fano varieties over number fields. In joint work with C. Frei, we developed a method that involves counting lattice points in definable sets in the o-minimal structure $\mathbb{R}_{\text{exp}}$ to verify the conjecture on given varieties over arbitrary number fields. In this talk I present the method with some applications.