Research in inertial fusion sciences and applications worldwide is making dramatic progress. The National Ignition Facility (NIF) in the US and the Laser MegaJoule (LMJ) in France are being built to achieve fusion ignition in the laboratory. Experiments that have been done on current Inertial Confinement Fusion (ICF) facilities in the US and around the world have demonstrated that the drive characteristics required for ignition are now well understood and a new plan for inertial fusion energy development has been put together by the community. Besides examining the conditions necessary for fusion ignition, targets were designed without fusion capsules. Equilibrium temperatures of hundreds of electron volts and megabar pressures were used to study astrophysical processes and measure equations of states at these extreme conditions. Recent studies of laser-matter interactions with femtosecond lasers have revealed some startling new phenomena due to the ability to achieve irradiances >1020 W cm-2. This paper will review recent results in fusion and high energy density science achieved by high intensity lasers at LLNL and will look ahead to what may achieved on NIF.