In this talk, I will introduce some recent works of invariant theory for CR manifolds. After a briefing in CR manifolds, some integral invariants will be introduced in the Heisenberg groups (as a flat model of CR manifolds). The invariants are not changed in the sense of the pseudo-hermitian transformation which can be considered as the rigid motions in the Heisenberg groups. We take the approach from Integral Geometry for convex bodies, but in our cases, the assumption of convexity is not necessarily needed. The applications can be implemented by the CR-version of the Crofton's formula and the containment problems with other development. Some recent development in the invariant theory for CR manifolds will also be discussed in the end of the talk.