We report high-pressure and high-temperature studies on a series of oxide garnets of chemical composition ${A}_{3}{B}_{2}{C}_{3}{\mathrm{O}}_{12}$. The members of this family investigated are gadolinium scandium gallium garnet (GSGG), gadolinium gallium garnet (GGG), and yttrium aluminum garnet (YAG). The GSGG and GGG are doped with both neodymium and chromium while the YAG is doped only with neodymium. Photoluminescence, synchrotron x-ray-diffraction, and laser heating studies were carried out in a diamond-anvil cell. Variety of optical sensors (ruby, Sm-doped YAG) and x-ray pressure marker (copper) were employed for pressure measurement. Pressure-induced amorphization was observed in GSGG at 58\ifmmode\pm\else\textpm\fi{}3 GPa and GGG at 84\ifmmode\pm\else\textpm\fi{}4 GPa by x-ray-diffraction studies. The photoluminescence studies show only gradual broadening of emission bands through the amorphization transition. On increasing pressure beyond amorphization, very broad and featureless emission bands were observed in the fluorescence spectra at 77\ifmmode\pm\else\textpm\fi{}2 GPa for GSGG and at 88\ifmmode\pm\else\textpm\fi{}2 GPa for GGG. Laser heating of the pressure-induced amorphous phase in GSGG caused recrystallization to the stable cubic phase. High-pressure x-ray study on YAG shows that it retains cubic phase up to 101\ifmmode\pm\else\textpm\fi{}4 GPa. A pressure-volume relation for each member of the oxide garnet at ambient temperatures is presented, structural transformation mechanisms, and application of oxide garnets as pressure sensors are also discussed.