Is torsion needed in a theory of gravity? A reappraisal

It is known that General Relativity ({\bf GR}) uses a Lorentzian Manifold $(M_4;g)$ as a geometrical model of the physical spacetime. The metric $g$ is required to satisfy Einstein's equations. Since the 1960s many authors have tried to generalize this model by introducing torsion. In this paper we discuss the present status of torsion in a theory of gravity. Our conclusion is that the general-relativistic model of the physical spacetime is sufficient for the all physical applications and it seems to be the best satisfactory.