Tuna, billfish, and oceanic sharks [hereafter referred to as ‘mobile oceanic fishes and sharks’ (MOFS)] are characterised by conservative life-history strategies and highly migratory behaviour across large, transnational ranges. Intense exploitation over the past 65 years by a rapidly expanding high-seas fishing fleet has left many populations depleted, with consequences at the ecosystem level due to top-down control and trophic cascades. Despite increases in both CITES and IUCN Red Listings, the demographic trajectories of oceanic sharks and billfish are poorly quantified and resolved at geographic and population levels. Amongst MOFS trajectories, those of tunas are generally considered better understood, yet several populations remain either overfished or of unknown status. MOFS population trends and declines therefore remain contentious, partly due to challenges in deriving accurate abundance and biomass indices. Two major management strategies are currently recognised to address conservation issues surrounding MOFS: (i) internationally ratified legal frameworks and their associated regional fisheries management organisations (RFMOs); and (ii) spatio-temporal fishery closures, including no-take marine protected areas (MPAs). In this context, we first review fishery-dependent studies relying on data derived from catch records and from material accessible through fishing extraction, under the umbrella of RFMO-administrated management. Challenges in interpreting catch statistics notwithstanding, we find that fishery-dependent studies have enhanced the accuracy of biomass indices and the management strategies they inform, by addressing biases in reporting and non-random effort, and predicting drivers of spatial variability across meso- and oceanic scales in order to inform stock assessments. By contrast and motivated by the increase in global MPA coverage restricting extractive activities, we then detail ways in which fishery-independent methods are increasingly improving and steering management by exploring facets of MOFS ecology thus far poorly grasped. Advances in telemetry are increasingly used to explore ontogenic and seasonal movements, and provide means to consider MOFS migration corridors and residency patterns. The characterisation of trophic relationships and prey distribution through biochemical analysis and hydro-acoustics surveys has enabled the tracking of dietary shifts and mapping of high-quality foraging grounds. We conclude that while a scientific framework is available to inform initial design and subsequent implementation of MPAs, there is a shortage in the capacity to answer basic but critical questions about MOFS ecology (who, when, where?) required to track populations non-extractively, thereby presenting a barrier to assessing empirically the performance of MPA-based management for MOFS. This sampling gap is exacerbated by the increased establishment of large (>10000 km2) and very large MPAs (VLMPAs, >100000 km2) - great expanses of ocean lacking effective monitoring strategies and survey regimes appropriate to those scales. To address this shortcoming, we demonstrate the use of a non-extractive protocol to measure MOFS population recovery and MPA efficiency. We further identify technological avenues for monitoring at the VLMPA scale, through the use of spotter planes, drones, satellite technology, and horizontal acoustics, and highlight their relevance to the ecosystem-based framework of MOFS management.