  We review the application of torsion in field theory. First we show how the
notion of torsion emerges in differential geometry. In the context of a Cartan
circuit, torsion is related to translations similar as curvature to rotations.
Cartan's investigations started by analyzing Einsteins general relativity
theory and by taking recourse to the theory of Cosserat continua. In these
continua, the points of which carry independent translational and rotational
degrees of freedom, there occur, besides ordinary (force) stresses,
additionally spin moment stresses. In a 3-dimensional continuized crystal with
dislocation lines, a linear connection can be introduced that takes the crystal
lattice structure as a basis for parallelism. Such a continuum has similar
properties as a Cosserat continuum, and the dislocation density is equal to the
torsion of this connection. Subsequently, these ideas are applied to
4-dimensional spacetime. A translational gauge theory of gravity is displayed
(in a Weitzenboeck or teleparallel spacetime) as well as the viable
Einstein-Cartan theory (in a Riemann-Cartan spacetime). In both theories, the
notion of torsion is contained in an essential way. Cartan's spiral staircase
is described as a 3-dimensional Euclidean model for a space with torsion, and
eventually some controversial points are discussed regarding the meaning of
torsion.
