B.E.Johnson introduced the bounded cohomology of groups (though the term "bounded cohomology" came later) and characterized the amenable groups by vanishing of bounded cohomology. We present the following characterization of Gromov hyperbolic groups by bounded cohomology: a finitely presented group G is hyperbolic if and only if all 2-dimensional cohomology classes of G are bounded for all coefficients. This boundedness of cocycles for hyperbolic groups (for real coefficients) was claimed by Gromov and was used by Connes and Moscovici to prove the Novikov conjecture for hyperbolic groups. Our characterization of hyperbolic groups resembles Johnson's characterization of amenable groups, though the proof is of course completely different. The main step in the proof is a combinatorial version of straightening that works for any hyperbolic group. Another application of similar combinatorial techniques is constructing a nice metric on any hyperbolic group that allows us to prove the Baum-Connes conjecture for hyperbolic groups (this result is a joint work with Guoliang Yu). In particular, this implies the Kadison-Kaplansky conjecture for torsion-free hyperbolic groups.