The first half of this talk will be a review of p-adic integration, focusing on the case of smooth varieties and varieties with quotient singularities and describing classical applications. The second half will be devoted to work in progress with Wyss & Ziegler, which concerns p-adic integrals on moduli spaces of linear nature and the connection to Donaldson–Thomas theory. I will describe applications of p-adic integration to certain symplectic moduli spaces, including Nakajima quiver varieties and moduli spaces of sheaves on a K3 surface.