We present a study of the different high-pressure polymorphs of GdVO4 and its stability. Powder x-ray diffraction and Raman experiments show a phase transition from a zircon- to a scheelite-type structure taking place at 6.8(4) GPa. Ab initio density functional theory calculations support this conclusion. The equations of state of these two phases are reported. In addition, we studied the pressure evolution of the Raman modes for the zircon and scheelite phases, showing good agreement between calculations and experiments. For the sake of completeness, we performed optical-absorption measurements up to 16 GPa, showing a band-gap collapse at the transition point. Beyond 20 GPa a second phase transition to a monoclinic fergusonite structure takes place as a consequence of a mechanical instability. A third transition is observed at around 29.3 GPa in Raman experiments. According to our calculations, this fourth polymorph corresponds to an orthorhombic structure described by space group Cmca. This phase involves an increase of the atomic coordination number of vanadium and gadolinium. The results are compared to those reported on isomorphic compounds.