We submit that, contrary to the standard view, gravitational waves do not carry energy-momentum. Analysing the four standard arguments on which the standard view rests - viz. the kinetic effects of a GW on a detector, Feynman’s Sticky Bead Argument, an application of Noether’s Theorem and a general perturbative approach – we find none of them to be successful: Pre-relativistic premises underlie each of them – premises that, as we argue, no longer hold in General Relativity. Finally, we outline a (...) GR-consistent interpretation of the effects and, in particular, the spin-down of binary systems. (shrink)