We study the effects of pressure on the structural, vibrational, and magnetic behavior of cuproscheelite. We performed powder x-ray diffraction and Raman spectroscopy experiments up to 27 GPa as well as ab initio total-energy and lattice-dynamics calculations. Experiments provide evidence that a structural phase transition takes place at 10 GPa from the low-pressure triclinic phase $(P\overline{1})$ to a monoclinic wolframite-type structure $(P2/c)$. Calculations confirmed this finding and indicate that the phase transformation involves a change in the magnetic order. In addition, the equation of state for the triclinic phase is determined: ${V}_{0}=132.8(2)\text{ }{\text{\AA{}}}^{3}$, ${B}_{0}=139(6)\text{ }\text{GPa}$, and ${B}_{0}^{\ensuremath{'}}=4$. Furthermore, experiments under different stress conditions show that nonhydrostatic stresses induce a second phase transition at 17 GPa and reduce the compressibility of ${\text{CuWO}}_{4}$, ${B}_{0}=171(6)\text{ }\text{GPa}$. The pressure dependence of all Raman modes of the triclinic and high-pressure phases is also reported and discussed.