  Fast Ignition Inertial Confinement Fusion is a variant of inertial fusion in
which DT fuel is first compressed to high density and then ignited by a
relativistic electron beam generated by a fast (< 20 ps) ultra-intense laser
pulse, which is usually brought in to the dense plasma via the inclusion of a
re-entrant cone. The transport of this beam from the cone apex into the dense
fuel is a critical part of this scheme, as it can strongly influence the
overall energetics. Here we review progress in the theory and numerical
simulation of fast electron transport in the context of Fast Ignition.
Important aspects of the basic plasma physics, descriptions of the numerical
methods used, a review of ignition-scale simulations, and a survey of schemes
for controlling the propagation of fast electrons are included. Considerable
progress has taken place in this area, but the development of a robust,
high-gain FI `point design' is still an ongoing challenge.
