The modern theory of cyclical fluctuations and its relevancy to actual processes in the global economy are discussed in the article. It points to the limited applicability of the theory to practical needs of households, businesses and governments. Possible directions of the theory evolution are considered: more focus on financial shocks, strengthening microeconomic foundations, selection of more homogeneous periods with specific features and shocks for analysis. The breakdown of post-war period into three relatively homogeneous sub-periods named "stationary regimes" is proposed. These sub-periods are separated on the basis of quantitative and qualitative analysis of the group of economic indicators. The global crisis of 2008—2009 is defined as a turning point between the 3rd and the expected 4th "stationary regimes". Assumptions are suggested concerning possible features of economic growth in the next "stationary regime" as well as their reflection in the theory of cycle.