Laser driven dynamic compression experiments play the central role in extreme pressure and density research, and are important to a number of fields, including planetary geophysics, material science, and inertial confinement fusion, benefit to improve understandings of properties of materials at extreme conditions and their applications. Recently laser driven compression techniques have been developing quickly together with laser facility, laser plasma interaction, target fabrication and diagnostic techniques. On contrast to other loading platform, it is good at ramp compression, decaying shock compression and complex loading path, and allows micro-scale probe combined with macro-scale measurements, ultra-high pressure and strain rate. This review summarizes this technique from the aspects of thermodynamics of compression, laser drive mechanism, laser drive experimental techniques and recent advances of extreme compression of materials.