  In the present work, we consider the existence, stability, and dynamics of
solitary waves in the nonlinear Dirac equation. We start by introducing the
Soler model of self-interacting spinors, and discuss its localized waveforms in
one, two, and three spatial dimensions and the equations they satisfy. We
present the associated explicit solutions in one dimension and numerically
obtain their analogues in higher dimensions. The stability is subsequently
discussed from a theoretical perspective and then complemented with numerical
computations. Finally, the dynamics of the solutions is explored and compared
to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger
equation. A few special topics are also explored, including the discrete
variant of the nonlinear Dirac equation and its solitary wave properties, as
well as the PT-symmetric variant of the model.
