M. Gromov introduced the notion of hyperbolic group. A finitely presented group \(G=<A;R>\) is said to be hyperbolic if there is a constant C such that a word w is equal to 1 in G iff it can be represented in the free group with the basis A as a product of \(\leq C\cdot length(w)\) conjugates of elements of the form r or \(r^{-1}\), where \(r\in R\). Such groups naturally arise in geometry; in particular, discrete isometry groups G of the hyperbolic space \(H^ n\) with compact \(H^ n/G\) are hyperbolic. As Gromov showed every hyperbolic group has solvable conjugacy problem. The author shows that hyperbolic groups are exactly those admitting finite presentations satisfying the following Dehn condition: every non-empty freely reduced word equal to 1 in the group contains more than a half of a defining relation. He also proves that in hyperbolic groups the following problems are decidable: the root problem, the order problem, the occurrence problem for cyclic subgroups, the solvability problem for quadratic equations. These results generalize the analogous known ones for small cancellation groups.