In this talk, I will start by presenting what KK-rigidity means and how I together with Chris Schafhauser have modified it to the dynamical setting for strongly outer actions on classifiable C*-algebras. This includes an application to the uniqueness of the Bernoulli shift on the CAR-algebra and Jiang-Su algebra for torsion-free amenable countable discrete groups. Then I will move towards the machinery leading up to the rigidity theorem, which includes some exposition on the cocycle category and classification of equivariant KK-lifts