Topological order, as a new kind of organization in many-body systems, cannot be characterized by local order parameters and long range correlations of local operators. We need to use a new set of quantum numbers to characterize topological order, such as ground state degeneracy, non-Abelian phases from modulo transformation, edge states, and pattern of long range entanglements. Due to the presence of long range entanglements, many traditional ways of constructing many-body states fail to produce topological ordered states. I will review several new ways to construct many-body states that may contain topological order.