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We provide a bird's eye view on developments in analyzing the long time,large crowd behavior of Cucker-Smale alignment dynamics. We consider a class of(fully-)discrete models, paying particular attention to general alignmentprotocols in which agents, with possibly time-dependent masses, are driven by alarge class of heavy-tailed communication kernels. The presence oftime-dependent masses allows, in particular, non-symmetric communication. Whilerevisiting known results in the literature, we also shed new light of variousaspects on the long time flocking/swarming behavior, driven by the decay ofenergy fluctuations and heavy-tailed connectivity. We also discuss the largecrowd dynamics in terms of the hydrodynamic description of Euler alignmentmodels.

Long time and large crowd dynamics of discrete Cucker-Smale alignment models