Fast ignition is an approach to inertial fusion in which precompressed fuel is ignited with an external heat source. This arrangement can, in principle, lead to higher gains than conventional ignition produced by stagnation of convergent flows. In addition, because ignition is separate from the implosion in fast ignition, hydrodynamic mix has less opportunity to quench ignition than in the conventional process. This paper introduces some of the basic ideas of fast ignition: ignition requirements, gain curves based on simple energetic models, and integrated gain models including hohlraum and implosion physics. Because possible gains in this approach are so large, it is possible to examine the use of fuels with small tritium fractions, the so-called "advanced fuels." In addition, the historical background of this field is discussed.