The Sato-Tate group of an abelian variety A of dimension g defined over a number field is a compact real Lie subgroup of the unitary simplectic group of degree 2g that conjecturally governs the limiting distribution of the normalized Frobenius elements in the Tate module of A. In previous joint work with Kedlaya, Rotger and Sutherland, it was shown that there are 52 groups (up to conjugation) that occur as Sato-Tate groups of abelian surfaces over number fields. In this talk I will present a classification of Sato-Tate groups of abelian threefolds over number fields based on ongoing work with Kedlaya and Sutherland.