In this review, we discuss the recent progress on the study of dynamic topological phenomena in quench dynamics. In particular, we focus on dynamic quantum phase transition and dynamic topological invariant, both of which are hinged upon the existence of fixed points in the dynamics. Further, the existence of these fixed points are topologically protected, in the sense that their existence are closely related to static topological invariants of pre- and post-quench Hamiltonians. We also discuss under what condition these dynamic topological phenomena are robust in non-unitary quench dynamics governed by non-Hermitian Hamiltonians. So far, dynamic topological phenomena have been experimentally observed in synthetic systems such as cold atomic gases, superconducting qubits, and linear optics. These studies extend our understanding of topological matter to the non-equilibrium regime.