On a macroscopic level we take general relativity as the appropriate theory of space-time and gravity. We will argue that, on a more microscopic level, in the Compton wavelength regime of elementary particles, there are good reasons for suspecting the presence of a torsion of space-time. A corresponding gaugetheoretical formalism related to the Poincaré group is reviewed, and the kinematical consequences of the presence of a torsion are worked out. In particular we discuss the operational meaning and the measurability of (...) torsion. The dynamics of torsion is left for a forthcoming article. (shrink)