Low-Energy Effective Action in N=4 Super Yang-Mills Theories

We review a recent progress in constructing low-energy effective action in N=4 super Yang-Mills theories. Using harmonic superspace approach we consider N=4 SYM in terms of unconstrained N=2 superfield and apply N=2 background field method to finding effective action for N=4 SU(n) SYM broken down to U(n)${}^{n-1}$. General structure of leading low-energy corrections to effective action is discussed.