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In this review we present a comprehensive discussion of peculiar velocityfield measured recently on very large scales with a novel method using X-raygalaxy clusters as tracers. The measurement is based on the kinematic componentof the Sunyaev-Zeldovich (KSZ) effect produced by Compton scattering of cosmicmicrowave background (CMB) photons off the hot intracluster gas, and uses alarge catalog of X-ray selected clusters and all-sky CMB maps obtained with theWMAP satellite. The method probes the dipole of the CMB temperature fieldevaluated at the cluster positions and within the apertures in which the CMBmonopole contribution vanishes, thereby isolating the signal remaining from theKSZ effect produced by coherently moving clusters. The detection of a highlysignificant dipole out to the depth of at least ~ 800 Mpc casts doubt on thenotion that gravitational instability from the observed mass distribution isthe sole -- or even dominant -- cause of the detected motions. Rather itappears that the flow may extend across the entire observable Universe.Possible implications include the possibility to constrain the primevalpreinflationary structure of space-time and its landscape, and/or the need formodifications of presently known physics (e.g. arising from ahigher-dimensional structure of gravity). We review these possibilities inlight of the measurements described here and specifically discuss the prospectsof future measurements and the issues they should resolve. We address theconsistency of these large-scale velocity measurements with those obtained onsmaller scales by studies using galaxies as tracers, and resolve thediscrepancies with two recent claims based on modified CMB analysis schemes.

Measuring bulk motion of X-ray clusters via the kinematic Sunyaev-Zeldovich effect: summarizing the "dark flow" evidence and its implications