  Torsion represents the most natural extension of General Relativity and it
attracted interest over the years in view of its link with fundamental
properties of particle motion. The bulk of the approaches concerning the
torsion dynamics focus their attention on their geometrical nature and they are
naturally led to formulate a non-propagating theory.
  Here we review two different paradigms to describe the role of the torsion
field, as far as a propagating feature of the resulting dynamics is concerned.
However, these two proposals deal with different pictures, i.e., a macroscopic
approach, based on the construction of suitable potentials for the torsion
field, and a microscopic approach, which relies on the identification of
torsion with the gauge field associated with the local Lorentz symmetry. We
analyze in some detail both points of view and their implications on the
coupling between torsion and matter will be investigated. In particular, in the
macroscopic case, we analyze the test-particle motion to fix the physical
trajectory, while, in the microscopic approach, a natural coupling between
torsion and the spin momentum of matter fields arises.
