I give a physical 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 show 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. Also, the stochastic aspects inherent in fluctuations lead to the breakdown of geometric scaling and of the BFKL approximation. Finally, I explain the diagrammatic interpretation of the particle number fluctuations as initiators of the Pomeron loops.