We discuss a general 'gauging' procedure to encode geometric reduction data into Topological Field Theories. This is done within the general AKSZ construction of such theories that we shall review first. We then continue by replacing the target space of this construction with the corresponding BFV model for constrained graded symplectic manifolds that we also review. Finally, we discuss the equivalence of the sigma model thus constructed with the one corresponding to the reduced geometry. We also discuss several examples in dimension (one,) two and three when the symmetries come from Lie group actions and systematically recover models already proposed in the literature. This is joint work with F. Bonechi and M. Zabzine.