Selection processes are believed to be an important evolutionary driver behind the successful establishment of nonindigenous species, for instance through adaptation for invasiveness (e.g. dispersal mechanisms and reproductive allocation). However, evidence supporting this assumption is still scarce. Genome scans have often identified loci with atypical patterns of genetic differentiation (i.e. outliers) indicative of selection processes. Using microsatellite- and AFLP-based genome scans, we looked for evidence of selection following the introduction of the mollusc Crepidula fornicata. Native to the northwestern Atlantic, this gastropod has become an emblematic invader since its introduction during the 19th and 20th centuries in the northeastern Atlantic and northeastern Pacific. We examined 683 individuals from seven native and 15 introduced populations spanning the latitudinal introduction and native ranges of the species. Our results confirmed the previously documented high genetic diversity in native and introduced populations with little genetic structure between the two ranges, a pattern typical of marine invaders. Analysing 344 loci, no outliers were detected between the introduced and native populations or in the introduced range. The genomic sampling may have been insufficient to reveal selection especially if it acts on traits determined by a few genes. Eight outliers were, however, identified within the native range, underlining a genetic singularity congruent with a well-known biogeographical break along the Florida. Our results call into question the relevance of AFLP genome scans in detecting adaptation on the timescale of biological invasions: genome scans often reveal long-term adaptation involving numerous genes throughout the genome but seem less effective in detecting recent adaptation from pre-existing variation on polygenic traits. This study advocates other methods to detect selection effects during biological invasions—for example on phenotypic traits, although genome scans may remain useful for elucidating introduction histories.