  This article reviews recent developments in quantum fluid dynamics and
quantum turbulence (QT) for superfluid helium and atomic Bose-Einstein
condensates. Quantum turbulence was discovered in superfluid $^4$He in the
1950s, but the field moved in a new direction starting around the mid 1990s.
Quantum turbulence is comprised of quantized vortices that are definite
topological defects arising from the order parameter appearing in Bose-Einstein
condensation. Hence QT is expected to yield a simpler model of turbulence than
does conventional turbulence. A general introduction to this issue and a brief
review of the basic concepts are followed by a description of vortex lattice
formation in a rotating atomic Bose-Einstein condensate, typical of quantum
fluid dynamics. Then we discuss recent developments in QT of superfluid helium
such as the energy spectra and dissipative mechanisms at low temperatures, QT
created by vibrating structures, and the visualization of QT. As an application
of these ideas, we end with a discussion of QT in atomic Bose-Einstein
condensates.
