I discuss the modern development of the analytic methods in the theory of hadrons. These methods are based on the operator product expansion and ascend to the SVZ sum rules elaborated 20 years ago. They allow one to relate a large variety of properties of the low-lying hadronic states and important regularities established in the hadronic world to a few vacuum condensates parametrizing the vacuum of quantum chromodynamics. A significant progress took place in deeper understanding of both, the conceptual foundations of the method, and its practical implementation and limitations. I review, from the modern standpoint, novel ideas of the QCD vacuum, various aspects of the operator product expansion, new applications of the SVZ sum rules, and their role among other competing approaches in the theory of hadrons.