Modern studies in two-dimensional conformal field theory and its applications to the physics of the 2D critical phenomena are reviewed. The bootstrap approach to conformal field theory based on the operator product algebra is consistently developed. Some exact solutions to the theory, including "minimal models" with c < 1 and a continuous set of models with c = 1 are given in detail. These models describe critical and multicritical points of various 2D statistical systems, the Ising model, the 3-state Potts model and the Ashkin-Teller model being among them. An alternative approach to conformal field theory, based on the modular invariance of the toroidal partition function ("modular bootstrap"), is also discussed.
