  Emergent order resulting from spontaneous symmetry breakings has been a
central topic in statistical physics. Active matter systems composed of
nonequilibrium elements exhibit a diverse range of fascinating phenomena beyond
equilibrium physics. One striking example is the emergent long-range
orientational order in two dimensions, which is prohibited in equilibrium
systems. The existence of long-range order in active matter systems was
predicted first by a numerical model and proven analytically by dynamic
renormalization group analysis. Experimental evidence for long-range order with
giant number fluctuations has been provided in some experimental systems
including microswimmers such as swimming bacteria and electrokinetic Janus
particles. In this review, we provide a pedagogical introduction to the
theoretical descriptions of long-range order in collective motion of active
matter systems and an overview of the experimental efforts in the two
prototypical microswimmer experimental systems. We also offer critical
assessments of how and when such long-range order can be achieved in
experimental systems. By comparing numerical, theoretical, and experimental
results, we discuss the future challenges in active matter physics.
