  Shear-free or asymptotically shear-free null geodesic congruences possess a
large number of fascinating geometric properties and to be closely related, in
the context of general relativity, to a variety of physically significant
affects. It is the purpose of this paper to develop these issues and find
applications in GR. The applications center around the problem of extracting
interior physical properties of an asymptotically flat space-time directly from
the asymptotic gravitational (and Maxwell) field itself in analogy with the
determination of total charge by an integral over the Maxwell field at infinity
or the identification of the interior mass (and its loss) by (Bondi's)
integrals of the Weyl tensor, also at infinity. More specifically we will see
that the asymptotically shear-free congruences lead us to an asymptotic
definition of the center-of-mass and its equations of motion. This includes a
kinematic meaning, in terms of the center of mass motion, for the Bondi
three-momentum. In addition, we obtain insights into intrinsic spin and, in
general, angular momentum, including an angular momentum conservation law with
well-defined flux terms. When a Maxwell field is present the asymptotically
shear-free congruences allow us to determine/define at infinity a
center-of-charge world-line and intrinsic magnetic dipole moment.
