Let X be a Fano variety with an associated height function defined over a number field. Manin's conjecture predicts that, after removing a thin set, the growth of the number of rational points of bounded height on X is controlled by certain geometric invariants (e.g. the Fujita invariant of X). I will talk about how to use birational geometric methods to study the behaviour of these invariants and propose a geometric description of the thin set in Manin's conjecture. Part of this is joint work with Brian Lehmann and Sho Tanimoto.