In this talk, I will report some recent work on the stability for a class of Caffarelli-Kohn-Nirenberg (CKN) inequalities in Euclidean spaces. By establishing a parameter family of Caffarelli-Kohn-Nirenberg identities, we prove sharp stability for a class of CKN inequalities (including the Heisenberg uncertainty principle) with optimal constants. Moreover, we also show that there exist extremal functions for these sharp stable CKN inequalities. This is joint work with C. Cazacu, J. Flynn and N. Lam.