Sato-Tate groups of genus 2 curves

We describe the analogue of the Sato-Tate conjecture for an abelian variety over a number field; this predicts that the zeta functions of the reductions over various finite fields, when properly normalized, have a limiting distribution predicted by a certain group theoretic construction related to Hodge theory, Galois images, and endomorphisms. After making precise the definition of the Sato-Tate group appearing in this conjecture, we describe the classification of Sato-Tate groups of abelian surfaces due to Fite Kedlaya Rotger Sutherland.