The talk is devoted to a brief survey of recent progress in constructing a low-energy effective action for N=4 supersymmetric Yang-Mills theory. We present a formulation of extended supersymmetric field models in N=2 harmonic superspace with manifest N=2 supersymmetry and describe N=4 super Yang-Mills theory in this framework. General structure of low-energy effective action in N=4 SYM theory and a procedure of its calculation are discussed. A non-renormalization theorem for this effective action is pointed out.