The search for exotic topological phases has become a most exciting pursuit in condensed matter physics.In parallel to the remarkable developments in solid state systems,the recent experimental realizations of spin-orbit interaction and synthetic gauge fields for cold atoms open new possibilities to study topological states with clean and fully controllable platforms.In this talk,I will discuss our recent proposals for the realization of topological states with cold atoms,and will particularly present a new technique introduced in our recent works which generically enables the realization of topological phases with minimal setups and based on realistic cold atom systems.I will show that this technique can be applied to many different situations,including 1D and 2D systems,with and without spin-orbit couplings,and such situations lead to different classes of topological states.The experimental issues,including the heating effects,will be discussed.