  We review numerical studies of quantum turbulence. Quantum turbulence is
currently one of the most important problems in low temperature physics and is
actively studied for superfluid helium and atomic Bose--Einstein condensates. A
key aspect of quantum turbulence is the dynamics of condensates and quantized
vortices. The dynamics of quantized vortices in superfluid helium are described
by the vortex filament model, while the dynamics of condensates are described
by the Gross--Pitaevskii model. Both of these models are nonlinear, and the
quantum turbulent states of interest are far from equilibrium. Hence, numerical
studies have been indispensable for studying quantum turbulence. In fact,
numerical studies have contributed in revealing the various problems of quantum
turbulence. This article reviews the recent developments in numerical studies
of quantum turbulence. We start with the motivation and the basics of quantum
turbulence and invite readers to the frontier of this research. Though there
are many important topics in the quantum turbulence of superfluid helium, this
article focuses on inhomogeneous quantum turbulence in a channel, which has
been motivated by recent visualization experiments. Atomic Bose--Einstein
condensates are a modern issue in quantum turbulence, and this article reviews
a variety of topics in the quantum turbulence of condensates e.g.
two-dimensional quantum turbulence, weak wave turbulence, turbulence in a
spinor condensate, $etc.$, some of which has not been addressed in superfluid
helium and paves the novel way for quantum turbulence researches. Finally we
discuss open problems.
