Quantum fluids such as superfluid helium and atomic Bose-Einstein condensates are governed by a macroscopic wavefunction. As a consequence, vorticity is not a continuous unconstrained field (as in ordinary fluids), but takes the form of individual vortex filaments of fixed circulation (proportional to Planck's constant). Mechanical, thermal or optical stirring can easily turn few such vortices into a turbulent tangle whose properties are currently being investigated by experiments and numerical simulations. In this talk I shall describe two problems in which the Gross-Pitaevksii equation is used to model vortex tangles. The first is the decay of multi-charged vortices in atomic Bose-Einstein condensates; the second is the formation of turbulence near the boundaries of channels in experiments with superfluid helium.