Collectivity in large and small systems formed in ultrarelativistic collisions

Collective flow of the final-state hadrons observed in ultrarelativistic heavy-ion collisions or even in smaller systems formed in high-multiplicity pp and p/d/$$^3$$He-nucleus collisions is one of the most important diagnostic tools to probe the initial state of the system and to shed light on the properties of the short-lived, strongly interacting many-body state formed in these collisions. Limited, in the initial years, to the study of mainly the directed and elliptic flows—the first two Fourier harmonics of the single-particle azimuthal distribution—this field has evolved in recent years into a much richer area of activity. This includes not only higher Fourier harmonics and multiparticle cumulants, but also a variety of other related observables, such as the ridge seen in two-particle correlations, flow decorrelation, symmetric cumulants and event-plane correlators which measure correlations between the magnitudes or phases of the complex flows in different harmonics, coefficients that measure the nonlinear hydrodynamic response, statistical properties, e.g. the non-Gaussianity of the flow fluctuations, etc. We present a Tutorial Review of the modern flow picture and the various aspects of the collectivity—an emergent phenomenon in quantum chromodynamics