  The Landau-Lifshitz-Gilbert (LLG) equation is a fascinating nonlinear
evolution equation both from mathematical and physical points of view. It is
related to the dynamics of several important physical systems such as
ferromagnets, vortex filaments, moving space curves, etc. and has intimate
connections with many of the well known integrable soliton equations, including
nonlinear Schr\"odinger and sine-Gordon equations. It can admit very many
dynamical structures including spin waves, elliptic function waves, solitons,
dromions, vortices, spatio-temporal patterns, chaos, etc. depending on the
physical and spin dimensions and the nature of interactions. An exciting recent
development is that the spin torque effect in nanoferromagnets is described by
a generalization of the LLG equation which forms a basic dynamical equation in
the field of spintronics. This article will briefly review these developments
as a tribute to Robin Bullough who was a great admirer of the LLG equation.
