This talk is devoted to broken and emerging scale invariance of turbulence. Pumping breaks the symmetry: the statistics of every mode explicitly depends on the distance from the pumping.  And yet the ratios of mode amplitudes, called Kolmogorov multipliers, are known to  approach scale invariant statistics away from the pumping. This emergent scale invariance deserves an explanation and a detailed study. We put forward the hypothesis that the invariance of multipliers is due to an extreme non-locality of their interactions (similar to appearance of a mean-field properties in the thermodynamic limit for systems with long-range interaction). We analyze this phenomenon in a family of models that connects two very different classes of systems: resonantly interacting waves and wave-free incompressible flows. The connection is  algebraic and turns into identity for properly discretized models. We show that this family provides a unique opportunity for an analytic (perturbative) study of emerging scale invariance in a system with strong interactions.