O-minimal structures are the realization of Grothendieck's program of tame topology and generalize semi-algebraic and sub-analytic geometry. In this talk i will describe the recent development of sheaf theory and cohomology theory in this context. These theories have applications ranging from a generalization of Hilbert's 5th problem, homological dimension of sheaves on real analytic manifolds and possibly also a generalization of some results of Suslin-Voevodsky on the algebraic singular homology of varieties over the complex numbers.