Upon colonizing new habitats invasive species face a series of new selection pressures as a result of changing abiotic conditions and novel biotic interactions with native species. These new selection pressures can be accommodated by different mechanism that act on different levels and across different time scales: 1) By changing transcriptomic profiles species can react by plasticity within individual physiological limitations. 2) Invasive populations can adapt by fixing beneficial genetic variants in response to the newly encountered selection pressures. Here, we compare the genomic and transcriptomic landscapes of two independent invasions of the Pacific Oyster Crassostrea gigas into the North Sea. In detail, we combine high density full genome resequencing and low density ddRAD on the genomic level with RNAseq on the transcriptomic level to reveal outlier loci (SNPs) indicative of adaptation, as well as transcriptomic profiles from a translocation experiment to show immediate physiological reactions. The low congruence between differentially regulated genes and outlier loci indicates that different processes act on the different time scales. By contrasting population outlier loci and population specific transcriptomic profiles we can thus identify relevant processes acting during different phases of the invasive process, which will allow to take a glimpse at the traits and processes characterizing successful invasions. Raw dd-RAD data is submitted here, raw RNA-seq data are in ArrayExpress (E-MTAB-9186).