Room-temperature Raman scattering was measured in CdWO4 up to 43 GPa. We report the pressure dependence of all the Raman-active phonons of the low-pressure wolframite phase. As pressure increases changes in the Raman spectra are detected at 20 and 35 GPa due to the onset of reversible structural phase transitions. We also report ab initio total-energy and lattice-dynamics calculations for the different phases of CdWO4. They helped us determine the crystalline structure of the high-pressure phases. Experimental and theoretical results suggest the coexistence of two structures from 20 to 35 GPa: one with tetragonal symmetry and another with triclinic symmetry. Beyond 35 GPa the monoclinic fergusonite is proposed as the structure of CdWO4. The pressure evolution of the lattice parameters and the atomic positions of wolframite CdWO4 are also theoretically calculated and an equation of state is reported.