Low-energy effective action in N=2 supersymmetric field theories

A new approach to computing the effective action in N = 2 and N = 4 supersy mmetric field theories is reviewed. It is based on the formulation of these theories in terms of unconstrained superfields in the harmonic superspace. The construction of superfield models of the N = 2 supersymmetric field th eory (hypermultiplet; the N = 2 supersymmetric Yang-Mills theory) is discus sed. The N = 2 background field method is expounded. Perturbative holomorph ic effective potential in the N = 2 models and nonholomorphic effective pot ential that determines the exact low-energy effective action in the N = 4 Y ang-Mills field theory is considered. Possible applications of the low-ener gy action in supersymmetric theories and some other open problems are discu ssed. The approach under consideration is compared with other approaches.