  We review the concept and definitions of the energy-momentum and angular
momentum of the gravitational field in the teleparallel equivalent of general
relativity (TEGR). The importance of these definitions is justified by three
major reasons. First, the TEGR is a well established and widely accepted
formulation of the gravitational field, whose basic field strength is the
torsion tensor of the Weitzenb\"ock connection. Second, in the phase space of
the TEGR there exists an algebra of the Poincar\'e group. Not only the
definitions of the gravitational energy-momentum and 4-angular momentum satisfy
this algebra, but also the first class constraints related to these definitions
satisfy the algebra. And third, numerous applications of these definitions lead
to physically consistent results. These definitions follow from a well
established Hamiltonian formulation, and rely on the idea of localization of
the gravitational energy. In this review we revisit the concept of
localizability of the gravitational energy, in light of results obtained in
recent years. We have studied the behaviour of free particles in the space-time
of plane fronted gravitational waves (pp-waves). Free particles are here
understood as particles that are not subject to external forces other than the
gravitational acceleration due to pp-waves. Since these particles acquire or
loose kinetic energy locally, the transfer of energy from or to the
gravitational field must also be localized. We consider this theoretical result
an important and definite argument in favour of the localization of the
gravitational energy-momentum, and by extension, of the gravitational 4-angular
momentum.
