Various topologically ordered states have interesting properties, such as (1) topological degeneracy and fractional statistics or non-abelian group statistics that can be used to realize a topological quantum computer ; (2) perfect conducting edge states that may have important device applications; (3) emergent gauge field and Fermi statistics that suggest a quantum information origin of elementary particles ; (4) topological entanglement entropy that reveals the entanglement origin of topological order, etc. Topological order is important in the study of several physical systems such as spin liquids, and the quantum Hall effect, along with potential applications to fault-tolerant quantum computation.