This review discusses new developments in shock compression science with a focus on molecular media. Some basic features of shock and detonation waves, nonlinear excitations that can produce extreme states of high temperature and high pressure, are described. Methods of generating and detecting shock waves are reviewed, especially those using tabletop lasers that can be interfaced with advanced molecular diagnostics. Newer compression methods such as shockless compression and precompression shock that generate states of cold dense molecular matter are discussed. Shock compression creates a metallic form of hydrogen, melts diamond, and makes water a superionic liquid with unique catalytic properties. Our understanding of detonations at the molecular level has improved a great deal as a result of advanced nonequilibrium molecular simulations. Experimental measurements of detailed molecular behavior behind a detonation front might be available soon using femtosecond lasers to produce nanoscale simulated detonation fronts.