First, the fast ignition of compressed fusion fuel is discussed in terms ofthe isochoric ignition model and two-dimensional simulations. Non-sphericalconfigurations and deuterium fuel ignited from a deuterium-tritium seed arealso investigated. Experiments and simulations for laser fast ignition arealso presented, in particular relativistic self-focusing, hole boring, thegeneration of electron beams as well as filamented electron transport andcollective stopping. Finally, recent experimental and numerical work oncone-guided fast ignition and fast ignition by laser-generated proton beamsis reviewed.