Abstract: In the early 70's Alberto Verjovsky conjectured that every co-dimension one Anosov flow on a manifold of dimension at least four is topologically equivalent to a suspension over hyperbolic total automorphism. In particular in dimension four, the conjecture says that there exists only one topological equivalence class of Anosov flows. This problem can be interpreted as part of one of Smale's problems: Which manifolds can support a hyperbolic dynamical system? In this talk we prove that this conjecture is true. Anosov flows are central examples of chaotic systems. We will give a general overview of the different type of Anosov flows and show how our result gives an important step toward a more general classification. We will also discuss some topological obstructions for a manifold to support such a system.