Metal hydrides(M-H) on solid surfaces, i.e., surface M-H, are ubiquitous but critical species in heterogeneous catalysis, and their intermediate roles have been proposed in numerous reactions such as(de)hydrogenation and alkanes activation, etc., however, the detailed spectroscopic characterizations remain challenging. Solid-state nuclear magnetic resonance(ssNMR) spectroscopy has become a powerful tool in surface studies, as it provides access to local structural characterizations at atomic level from multiple views, with comprehensive information on chemical bonding and spatial structures. In this review, we summarized and discussed the latest research developments on the successful application of ssNMR to characterize surface M-H species on solid catalysts including supported single-site heterogeneous catalysts, bulk metal oxides and metal-modified zeolites. We also discussed the opportunities and challenges in this field, as well as the potential application/development of state-of-the-art ssNMR technologies to enable further exploration of metal hydrides in heterogeneous catalysis.