The heating of plasmas by fast ions, with a focus on Neutral Beam Injection (NBI), is reviewed. First, the need of auxiliary heating and current drive systems in fusion machines is outlined. For the particular case of tokamaks, the limitations of ohmic heating are discussed. The different ways of generating fast particles in plasmas are presented. The principle of operation of neutral beam injectors is explained. Positive-ion (PNBI) and negativeion (NNBI) based concepts are discussed. Next, the physical processes by which the beam transfers energy to the plasma, namely ionisation and slowing-down are described. For both, an elementary theory is given, whereby simple approximations to the distribution functions of beam injected ions and of alpha particles in reactors are obtained. Applications of NBI to heating, current drive and rotation drive are reviewed and the prospects of NBI for ITER are commented.