In many species, polymorphic genomic inversions underlie complex phenotypic polymorphisms and facilitate local adaptation in the face of gene flow. Multiple polymorphic inversions can co-occur in a genome, but the prevalence, evolutionary significance, and limits to complexity of genomic inversion landscapes remain poorly understood. Here, we examine genome-wide genetic variation in one of Europe's most destructive forest pests, the spruce bark beetle Ips typographus, scan for polymorphic inversions, and test whether inversions are associated with key traits in this species. We analyzed 240 individuals from 18 populations across the species' European range and, using a whole-genome resequencing approach, identified 27 polymorphic inversions covering approximately 28% of the genome. The inversions vary in size and in levels of intra-inversion recombination, are highly polymorphic across the species range, and often overlap, forming a complex genomic architecture. We found no support for mechanisms such as directional selection, overdominance and associative overdominance that are often invoked to explain the presence of large inversion polymorphisms in the genome. This suggests that inversions are either neutral or maintained by the combined action of multiple evolutionary forces. We also found that inversions are enriched in odorant receptor genes encoding elements of recognition pathways for host plants, mates, and symbiotic fungi. Our results indicate that the genome of this major forest pest of growing social, political, and economic importance harbors one of the most complex inversion landscapes described to date and raise questions about the limits of intraspecific genomic architecture complexity.