In this talk, we mainly study derivations, biderivations and triple derivations on Jordan algebras. Firstly, the sufficient and necessary conditions for their derivation algebras being simple are given. As an application, triple derivations of derivation algebras of semi-simple Jordan algebras are studied. Then we give a theorem about the relationship between biderivations and centroid of Jordan algebras and show that triple derivations are all derivations on Jordan algebras under some assumptions. Moreover, we also give a theorem about triple homomorphisms on Jordan algebras. This talk is a report on joint work with Yao Ma and Chenrui Yao.