A fascinating aspect of collective dynamics is self-organization of small-scale interactions into high-order structures with larger-scale patterns. In different contexts these are clusters which take the form of flocks, swarms, consensus, synchronized states etc. In this talk I will survey recent mathematical developments in alignment dynamics, which is driven by the tendency of steering towards average headings. A main question of interest is how different alignment kernels affect the large-crowd, long-time dynamics. We discuss how short- vs. long-range interactions dictate the large-crowd emergent behavior, and the role of pressure away thermal equilibrium