Many estimates in analysis  have certain “common structures” which makes it possible to obtain them with  what is now called Bellman function method. Originally the method appeared in control theory (stochastic or deterministic), however its systematic use  in harmonic analysis or probability started only recently  in works of Burkholder where he obtained the sharp constants in Lp estimates of martingale transforms. I will speak about Bellman functions, and in particular I will illustrate solutions of a class of extremal problems on BMO space using Bellman function technique.