Conformal field theories in various dimensions are rich mathematical objects encoding a wide variety of physical phenomena. For example, they describe the so-called second-order phase transitions and provide a non-perturbative window into quantum gravity via the AdS/CFT correspondence. The last decade has seen a rapid development of an axiomatic approach to conformal field theories, known as the conformal bootstrap. Among other things, this has led to the most precise determination of the critical exponents of the 3D Ising model currently available. In my talk, I will review the main ideas underlying the conformal bootstrap, focusing on the interplay between analytical and numerical approaches.