Range expansions are extremely common, but have only recently begun to attract attention in terms of their genetic consequences. As populations expand, demes at the wave front experience strong genetic drift, which is expected to reduce genetic diversity and potentially cause ‘allele surfing’, where alleles may become fixed over a wide geographical area even if their effects are deleterious. Previous simulation models show that range expansions can generate very strong selective gradients on dispersal, reproduction, competition and immunity. To investigate the effects of range expansion on genetic diversity and adaptation, we studied the population genomics of the bank vole (Myodes glareolus) in Ireland. The bank vole was likely introduced in the late 1920s and is expanding its range at a rate of ~2.5 km/year. Using genotyping-by-sequencing, we genotyped 281 bank voles at 5979 SNP loci. Fourteen sample sites were arranged in three transects running from the introduction site to the wave front of the expansion. We found significant declines in genetic diversity along all three transects. However, there was no evidence that sites at the wave front had accumulated more deleterious mutations. We looked for outlier loci with strong correlations between allele frequency and distance from the introduction site, where the direction of correlation was the same in all three transects. Amongst these outliers, we found significant enrichment for genic SNPs, suggesting the action of selection. Candidates for selection included several genes with immunological functions and several genes that could influence behaviour.