Species invasions cause significant ecological and economic damage, and genetic information is important to understanding and managing invasive species. In the ocean, many invasive species have high dispersal and gene flow, lowering the discriminatory power of traditional genetic approaches. High-throughput sequencing holds tremendous promise for increasing resolution and illuminating the relative contributions of selection and drift in marine invasion, but has not yet been used to compare the diversity and dynamics of a high-dispersal invader in its native and invaded ranges. We test a transcriptome-based approach in the European green crab (Carcinus maenas), a widespread invasive species with high gene flow and a well-known invasion history, in two native and five invasive populations. A panel of 10,809 transcriptome-derived nuclear SNPs identified significant population structure among highly bottlenecked invasive populations that were previously undifferentiated with traditional markers. Comparing the full data set and a subset of 9,246 putatively neutral SNPs strongly suggested that non-neutral processes are the primary driver of population structure within the species' native range, while neutral processes appear to dominate in the invaded range. Non-neutral native range structure coincides with significant differences in intraspecific thermal tolerance, suggesting temperature as a potential selective agent. These results underline the importance of adaptation in shaping intraspecific differences even in high-gene flow marine invasive species. They also demonstrate that high-throughput approaches have broad utility in determining neutral structure in recent invasions of such species. Together, neutral and non-neutral data derived from high-throughput approaches may increase understanding of invasion dynamics in high-dispersal species. This article is protected by copyright. All rights reserved.