  A concise discussion of spin-1/2 field equations with a special focus on
Majorana spinors is presented. The Majorana formalism which describes massive
neutral fermions by the help of two-component or four-component spinors is of
fundamental importance for the understanding of mathematical aspects of
supersymmetric and other extensions of the Standard Model of particle physics,
which may play an increasingly important role at the beginning of the LHC era.
The interplay between the two-component and the four-component formalism is
highlighted in an introductory way. Majorana particles are predicted both by
grand unified theories, in which these particles are neutrinos, and by
supersymmetric theories, in which they are photinos, gluinos and other states.
