Smale's classification conjecture for Anosov diffeomorphisms

Let $M$ be a closed manifold and let $f:M\to M$ be an Anosov diffeomorphism. A hyperbolic affine infra-nil-automorphism is an affine automorphism of an infra-nil-manifold whose linear part is hyperbolic. Smale's conjecture. Every Anosov diffeomorphism of a closed manifold is topologically conjugate to a hyperbolic affine infra-nil-automorphism. This conjecture proposes a universal algebraic model for Anosov diffeomorphisms. The paper recalls related classification results for Anosov diffeomorphisms on infra-nil-manifolds, but the stated classification for all closed manifolds is not resolved here.