Abstract. Anisotropic flow measurements play a crucial role in understanding the physics and bulk properties of the system created in heavy ion collisions. In this talk I briefly review the most important results obtained so far, recent developments in the analysis techniques and the interpretation of the results, and what should we expect next, both at RHIC and LHC. I also discuss event anisotropies sensitive to the strong parity violation effects.Analysis of the event anisotropies (anisotropic flow) in multiparticle production in non-central nuclear collisions appeared to be one of the most informative paths in understanding the physics and characterizing the properties of the dense and hot strongly interacting medium. It has been observed a continuous increase in the value of in-plane elliptic flow (v 2 > 0) [1] from the top AGS energies to RHIC. At RHIC, strong elliptic flow [2] comparable in strength to the predictions of ideal hydrodynamics, and the hadronization via quark coalescence following from constituent quark number scaling of differential flow [3,4], together with the jet quenching, are the key ingredients in the picture of sQGP (strongly coupled Quark Gluon Plasma).The field is rapidly developing and evolving. From the "discovery phase" of the first years of RHIC operations it has been transforming into detailed quantitative description of the sQGP phase and subsequent hadronization. The plots of v 2 /ε vs particle density [3,5,6] that have been extensively used in the assessment of the level of thermalization reached in the relativistic nuclear collisions and applicability of ideal hydrodynamics comes under scrutiny: are the measurements of elliptic flow precise enough, are the anisotropies what we think they are and how much are they modified by fluctuation processes? When comparing to hydrodynamical calculations, are the proper initial conditions used in the calculations? Could it be that we have missed some important physics building the models? In the last couple years significant progress has been reached answering each and every of these questions. The role of viscosity, flow fluctuations, initial conditions (eccentricity and initial flow (velocity) field) are a few questions to report in this review. I also discuss preliminary measurements of azimuthal "out-of-plane" anisotropies that are related to one of the fundamental questions of the strong parity violation. Finally, I briefly overview future measurements at RHIC and arXiv:0805.1351v1 [nucl-ex]