  Torsion appears in literature in quite different forms. Generally, spin is
considered to be the source of torsion, but there are several other
possibilities in which torsion emerges in different contexts. In some cases a
phenomenological counterpart is absent, in some other cases torsion arises from
sources without spin as a gradient of a scalar field. Accordingly, we propose
two classification schemes. The first one is based on the possibility to
construct torsion tensors from the product of a covariant bivector and a vector
and their respective space-time properties. The second one is obtained by
starting from the decomposition of torsion into three irreducible pieces. Their
space-time properties again lead to a complete classification. The
classifications found are given in a U_4, a four dimensional space-time where
the torsion tensors have some peculiar properties. The irreducible
decomposition is useful since most of the phenomenological work done for
torsion concerns four dimensional cosmological models. In the second part of
the paper two applications of these classification schemes are given. The
modifications of energy-momentum tensors are considered that arise due to
different sources of torsion. Furthermore, we analyze the contributions of
torsion to shear, vorticity, expansion and acceleration. Finally the
generalized Raychaudhuri equation is discussed.
