  This article surveys recent progress of results in topology and dynamics
based on techniques of closed one-forms. Our approach allows us to draw
conclusions about properties of flows by studying homotopical and cohomological
features of manifolds. More specifically we describe a Lusternik - Schnirelmann
type theory for closed one-forms, the focusing effect for flows and the theory
of Lyapunov one-forms. We also discuss recent results about cohomological
treatment of the invariants cat(X, \xi) and cat^1(X, \xi) and their explicit
computation in certain examples.
