The Hopf-Rinow theorem is a fundamental result in Riemannian geometry relating metric completeness, properness, and geodesic completeness. We recall the many reasons why it does not hold in Lorentzian geometry. Then we present our joint work with García-Heveling relating global hyperbolicity and completeness of the null distance and show that and how this result can be viewed as an extension of the metric part of the Hopf-Rinow theorem to Lorentzian geometry. We end with some thoughts about the semi-Riemannian setting.