High energy density physics(HEDP) is a rapidly growing frontier field,in which new physical phenomena are rich and important applications have been applied or prospected. The matter of high energy density is normal in universe. However,with the developments of high-power laser,Z-pinch,and ion accelerator facility,it is feasible to create such matter in laboratories. New developments and important scientific problems of high-power laser-based HEDP particularly on the fast ignition of inertial confinement fusion and laboratory astrophysics are briefly introduced.