Over complex numbers, the famous global Torelli theorem for K3 surfaces says that two integral Hodge isometric K3 surfaces are isomorphic. Recently, Huybrechts has shown that two rational Hodge isometric K3 surfaces are twisted derived equivalent. This is called the twisted derived Torelli theorem for K3. Natural questions arise for abelian varieties. In this talk, I will talk about the twisted derived equivalence for abelian surfaces, including the twisted derived Torelli theorem for abelian surfaces (over all fields) and its applications. This is a joint work with Haitao Zou.