Topological orders are non-symmetry breaking phases of matter, which provide a new paradigm in condensed-matter physics. Their characterization is a major open problem, although considerable progress has been made since the proposal of the topological entanglement entropy. In this talk I will review how topological orders have been proposed to serve as robust quantum memories. Then the dynamical stability of topologically ordered quantum states will be examined. Conditions will be derived on the type of dynamical evolution that allows quantum recurrence and preservation of the initial topological order.