  We review the recent results on development of vector models of spin and
apply them to study the influence of spin-field interaction on the trajectory
and precession of a spinning particle in external gravitational and
electromagnetic fields. The formalism is developed starting from the Lagrangian
variational problem, which implies both equations of motion and constraints
which should be presented in a model of spinning particle. We present a
detailed analysis of the resulting theory and show that it has reasonable
properties on both classical and quantum level. We describe a number of
applications and show how the vector model clarifies some issues presented in
theoretical description of a relativistic spin: A) One-particle relativistic
quantum mechanics with positive energies and its relation with the Dirac
equation and with relativistic {\it Zitterbewegung}; B) Spin-induced non
commutativity and the problem of covariant formalism; C) Three-dimensional
acceleration consistent with coordinate-independence of the speed of light in
general relativity and rainbow geometry seen by spinning particle; D)
Paradoxical behavior of the Mathisson-Papapetrou-Tulczyjew-Dixon equations of a
rotating body in ultra relativistic limit, and equations with improved
behavior.
