  The present article reviews the recent developments in the physics of quantum
turbulence. Quantum turbulence (QT) was discovered in superfluid $^4$He in the
1950s, and the research has tended toward a new direction since the mid 90s.
The similarities and differences between quantum and classical turbulence have
become an important area of research. QT is comprised of quantized vortices
that are definite topological defects, being expected to yield a model of
turbulence that is much simpler than the classical model. The general
introduction of the issue and a brief review on classical turbulence are
followed by a description of the dynamics of quantized vortices. Then, we
discuss the energy spectrum of QT at very low temperatures. At low wavenumbers,
the energy is transferred through the Richardson cascade of quantized vortices,
and the spectrum obeys the Kolmogorov law, which is the most important
statistical law in turbulence; this classical region shows the similarity to
conventional turbulence. At higher wavenumbers, the energy is transferred by
the Kelvin-wave cascade on each vortex. This quantum regime depends strongly on
the nature of each quantized vortex. The possible dissipation mechanism is
discussed. Finally, important new experimental studies, which include
investigations into temperature-dependent transition to QT, dissipation at very
low temperatures, QT created by vibrating structures, and visualization of QT,
are reviewed. The present article concludes with a brief look at QT in atomic
Bose-Einstein condensates.
