In the high pressure laboratory at BARC, we are pursuing a program to study the behaviour of materials under static and dynamic pressures. Theoretical component has been an integral part for guiding and interpreting new experiments. The initial phase of such efforts was devoted to the development of equation of state models at arbitrary temperatures and matter densities. With the advent of diamond anvil cell device and the simultaneous provision for laser heating of the compressed samples for static high pressure studies, and with the improvements of the diagnostic techniques in dynamic shock methods, the focus of our studies switched over to the predictions and interpretations of phase transitions. Often these efforts have led to intense experimental studies and sometimes helped in resolving the controversies in data. We adopted the first principles electronic structure calculations for high pressure studies. Our work on the electronic topological transition in zinc led to many experimental and theoretical investigations. The results of electronic structure changes in similar metal cadmium shall be compared with existing understanding in Zn under pressure. Our studies on Nb and other compounds like intermetallics and borocarbides have revealed interesting electronic structure changes under pressure. However, the electronic structure based investigations of structural stabilities at high pressures involve tedious trial and error effort, which is avoided in theab initio molecular dynamics simulations. The current status of our efforts in the use of this technique is illustrated with the example of quasicrystal based clusters.