AimBiogeographic boundaries and genetic structuring have important effects on the inferences and interpretation of effective population size (Ne) temporal variations, a key genetics parameter. We reconstructed the historical demography and divergence history of a vulnerable coastal high‐trophic shark using population genomics and assessed our ability to detect recent bottleneck events.LocationWestern and Central Indo‐Pacific (IPA), Western Tropical Atlantic (WTA) and Eastern Tropical Pacific (EPA).TaxonCarcharhinus leucas (Müller & Henle, 1839).MethodsA DArTcap™ approach was used to sequence 475 samples and assess global genetic structuring. Three demographic models were tested on each population, using an ABC‐RF framework coupled with coalescent simulations, to investigate within‐cluster structure. Divergence times between clusters were computed, testing multiple scenarios, with fastsimcoal. Ne temporal variations were reconstructed with STAIRWAYPLOT. Coalescent simulations were performed to determine the detectability of recent bottleneck under the estimated historical trend for datasets of this size.ResultsThree genetic clusters corresponding to the IPA, WTA and EPA regions were identified, agreeing with previous studies. The IPA presented the highest genetic diversity and was consistently identified as the oldest. No significant within‐cluster structuring was detected. Ne increased globally, with an earlier onset in the IPA, during the last glacial period. Coalescent simulations showed that weak and recent bottlenecks could not be detected with our dataset, while old and/or strong bottlenecks would erase the observed ancestral expansion.Main ConclusionsThis study further confirms the role of marine biogeographic breaks in shaping the genetic history of large mobile marine predators. Ne historical increases in Ne are potentially linked to extended coastal habitat availability. The limited within‐cluster population structuring suggests that Ne can be monitored over ocean basins. Due to insufficient amount of available genetic data, it cannot be concluded whether overfishing is impacting Bull Shark genetic diversity, calling for whole‐genome sequencing.