Contents  
1. Introduction  
2. Classification and Statements of the Surveyed Results  
3. Classification of Anosov Diffeomorphisms  
4. Integrability of the Invariant Bundles  
5. Reebless Foliations  
6. Interlude: Weak Partial Hyperbolicity  
7. Classification of Foliations in Certain 3-Dimensional Manifolds  
8. Leaf Conjugacy in Certain 3-Manifolds  
9. Euclidean Geometry, Not Isotopic to Anosov  
10. Euclidean Geometry, Isotopic to Anosov  
11. Nil Geometry  
12. Sol Geometry  
13. Seifert Spaces and Beyond  
14. Other Classification Results  