In many technological and scientific applications it is desirable to accurately determine the off-Hugoniot isentropic response of materials at ultra-high pressures. Although unloading isentropes can be determined from unloading profiles, experimental techniques for measuring compressive isentropic response have been extremely limited. A brief summary is presented of the various techniques that have been developed for isentropically compressing materials to high pressure. A new technique is also discussed, which shows considerable promise for performing isentropic compression experiments with smooth ramp waves to multi-Mbar pressures. This approach uses the high current densities produced with fast pulsed power accelerators to create continuous magnetic loading to a few hundred kbar in the present study over time intervals of 100 ns. The method has been successfully applied on copper and iron to determine the isentropic compression curve in copper and evaluation of the kinetic properties of the alpha-epsilon phase transition in iron. ©2000 American Institute of Physics.