**Dimension of harmonic measures in hyperbolic spaces**

We discuss random walks on groups acting on hyperbolic spaces (e.g. the PoincarĂ© disk), and their limiting behaviour on the boundary. The limiting distribution of the random walk (the harmonic measure) is of particular interest for description of bounded harmonic functions on the group (the Poisson boundary). We consider the Hausdorff dimension of harmonic measure on the boundary and give a formula in terms of the entropy and the drift under a general moment condition. Related recent results are also discussed during the talk.