  Active fluids exhibit spontaneous flows with complex spatiotemporal
structure, which have been observed in bacterial suspensions, sperm cells,
cytoskeletal suspensions, self-propelled colloids, and cell tissues. Despite
occurring in the absence of inertia, chaotic active flows are reminiscent of
inertial turbulence, and hence they are known as active turbulence. Here, we
survey the field, providing a unified perspective over different classes of
active turbulence. To this end, we divide our review in sections for systems
with either polar or nematic order, and with or without momentum conservation
(wet/dry). Comparing to inertial turbulence, we highlight the emergence of
power-law scaling with either universal or non-universal exponents. We also
contrast scenarios for the transition from steady to chaotic flows, and we
discuss the absence of energy cascades. We link this feature to both the
existence of intrinsic length scales and the self-organized nature of energy
injection in active turbulence, which are fundamental differences with inertial
turbulence. We close by outlining the emerging picture, remaining challenges,
and future directions.
