We have conducted high-pressure x-ray diffraction and Raman spectroscopic studies on the CdCr2Se4 spinel at room temperature up to 42 GPa. We have resolved three structural transitions up to 42 GPa, i.e., the starting Fd3m phase transforms at ∼11GPa into a tetragonal I41/amd structure, an orthorhombic distortion was observed at ∼15GPa, whereas structural disorder initiates beyond 25 GPa. Our ab initio density functional theory studies successfully reproduced the observed crystalline-to-crystalline structural transitions. In addition, our calculations propose an antiferromagnetic ordering as a potential magnetic ground state for the high-pressure tetragonal and orthorhombic modifications, compared with the starting ferromagnetic phase. Furthermore, the computational results indicate that all phases remain insulating in their stability pressure range, with a direct-to-indirect band gap transition for the Fd3m phase taking place at 5 GPa. We attempted also to offer an explanation behind the peculiar first-order character of the Fd3m(cubic)→I41/amd (tetragonal) transition observed for several relevant Cr spinels, i.e., the sizeable volume change at the transition point, which is not expected from space group symmetry considerations. We detected a clear correlation between the cubic-tetragonal transition pressures and the next-nearest-neighbor magnetic exchange interactions for the Cr-bearing sulfide and selenide members, a strong indication that the cubic-tetragonal transitions in these systems are principally governed by magnetic effects.