[en] This review contains a detailed description of methods of calculating ultraviolet divergences in two-dimensional nonlinear theories. The basic notions of the geometry of Riemannian manifolds are given, and the concept of the generalized renormalizability of sigma models is introduced. The covariant background-field method in nonlinear theories is described. The problem of infrared divergences and methods of removing them are discussed. The methods are illustrated by two-loop calculations in bosonic sigma models with the Wess-Zumino term and by four- and five-loop calculations in N=1 and N=2 supersymmetric sigma models. The role of Ricci-flat manifolds in obtaining conformally invariant sigma models is discussed in the concluding section. 72 refs., 9 figs., 2 tabs