ThisTurbulencequantum chapter introduces quantum turbulence - the turbulence of a quantum fluid. It is in this context that the dynamical effects described in the previous chapter (Kelvin waves, vortex reconnections, sound emission, etc.) come together. We start by describing turbulence in superfluid helium generated by heat transfer. This is the form of quantum turbulence which was discovered first, and is clearly quite different from ordinary turbulence. Then, after reviewing the main properties of three-dimensional (3D) turbulence in ordinary classical viscous fluids governed by the Navier-Stokes equation, we highlight the similarities and the differences between classical turbulence and quantum turbulence, focusing on the consequences of the quantisation of the circulation. In particular, we identify three different types of quantum turbulence: the Kolmogorov type, the Vinen type and turbulence in atomic Bose-Einstein condensates. Finally, we consider two-dimensional (2D) turbulence, which is very different from its 3D counterpart. In ordinary fluids this difference manifests itself as the tendency of large-scale structures to emerge from the small-scale disorder, a well-known example being Jupiter’s Great Red Spot. In the context of quantised vorticity, this phenomenon is understood in terms of negative absolute temperatures, as proposed by Onsager and recently verified in experiments with atomic condensates.