I present a pedagogical discussion of the influence of particle number fluctuations on the high energy evolution in QCD. I emphasize the event-by-event description and the correspondence with the problem of “fluctuating pulled fronts” in statistical physics. I explain that the correlations generated by fluctuations reduce the phase space for BFKL evolution up to saturation. Because of that, the evolution slows down, and the rate for the energy increase of the saturation momentum is considerably decreased. I discuss the diagrammatic interpretation of the particle number fluctuations in terms of pomeron loops.