Since 2009, the Inertial Confinement Fusion Program (ICF) at Lawrence Livermore National Laboratory has been conducting experiments at the National Ignition Facility (NIF), with the eventual goal of igniting DT plasma. This requires using the 1.8 MJ of energy in the NIF’s 192 laser beams to compress BB-sized capsules containing DT fuel and form a central DT “hot spot” with conditions similar to those at the center of the sun. Under these conditions DT fuses rapidly to produce a 14 MeV neutron, which escapes, and a 3.5 MeV alpha particle, which deposits its energy in the hot spot, provided it has sufficient areal density (greater than 0.2 g/cm2). If the self-heating from the alpha particles is strong enough it will outstrip cooling mechanisms and the plasma temperature will rapidly bootstrap to ignition. The alpha heating process has been demonstrated for the first time in the laboratory, resulting in roughly a doubling of the fusion yield to about 26 kJ from DT hot spots with densities of about 50,000 Kg/m3 and temperatures of about 50 million Kelvin, corresponding to pressures of about 200 billion atmospheres. Ignition, however, will require even better implosions, with roughly a factor of two higher pressures, amplifying yield by about a hundred times. Data indicate that making the implosions more spherical will be an important, although not straightforward, step toward this; ignition capsules on the NIF must be made to converge by more than a factor of about 30 at speeds exceeding about 350 km/s while remaining largely spherical. The NIF attempts to do this by carefully directing its 192 laser beams inside a pencil-eraser sized cylindrical X-ray oven – a hohlraum – creating a thermal X-ray bath of more than 300 million Kelvin. The X-rays ablate the capsule’s outer surface, generating approximately 100 million atmospheres of pressure, which must be uniform to better than about 1 percent to compress the fuel with adequate sphericity. In this presentation we will review the key physics of X-ray-driven ICF on the NIF, together with the status of current understanding (and some mysteries) gleaned from the data accumulated by a host of sophisticated diagnostics. We also will discuss some of the lines of investigation that are being pursued to improve our understanding and, hopefully, target performance.