Strongly interacting 4-dimensional quantum field theories (QFT), are of paramount importance for the description of Nature, but are very
hard to study. We still have very poor set of analytic tools to analyze their non-perturbative dynamics, to go beyond Feynman
perturbation theory and renormalization group. On the other hand, we have a big variety of exactly solvable, or integrable, 2-dimensional
QFTs, where we can compute analytically, or with great precision numerically, genuinely non-perturbative quantities. Can we apply this
knowledge for the study of 4-dimensional theories? In the past 20 years, there have been developed new analytic methods of studying the
strong coupling regime of at least a handful of these theories, using the AdS/CFT correspondence. The most remarkable of the QFTs is the
maximally supersymmetric Yang-Mills theory, called N=4 SYM. Its string dual allows to penetrate into the mystery of its strong coupling
behavior. Moreover the dual string sigma model, at least in the absence of string interactions, represents a particular integrable QFT and
hence we have a unique possibility to study N =4 SYM at any coupling, at least in a special large Nc ('t Hooft) limit. After quick overview of
integrable (1+1)-dimensional systems, I will demonstrate how this 2D integrability led to the solution of the problem of spectrum of
anomalous dimensions of N =4 SYM. I will illustrate it by particular non-perturbative results and mention some interesting limits of N =4
SYM, such as fishnet conformal field theory.