Diamond anvil cells (DAe are extensively utilized in the study of material properties at extreme conditions of pressures and temperatures. The pressures in excess of 400 GPa and temperatures in excess of 4000 K have been reported in DAC devices. Most studies on the optimization of diamond geometry and gasket materials used in diamond anvil cell devices have been carried out by trial and error using experimental high pressure data. This monograph addresses design and optimization issues in DAC using finite element modeling (FEM) and computational analysis. The computational approach is centered around the recent advances in the growth of isotopically enriched layers on diamond anvil and their use as pressure sensor in diamond anvil cell devices. In particular, the diamond layer of 6 microns in thickness grown on top of existing anvil has been demonstrated to serve as a universal pressure sensor to 156 GPa. The basic idea is that if a thin enough pressure sensor can be fabricated then the calibration of this sensor is independent of the stress or strain distribution in the diamond anvil cell device.