In many species, polymorphic inversions underlie complex phenotypic polymorphisms and appear to 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 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 involved in key adaptations in this species. We sampled 244 individuals from 18 populations across the species' European range and, using a whole-genome resequencing approach, identified 27 polymorphic inversions covering at least 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 an extremely complex genomic architecture. We show that the heterogeneous inversion landscape is likely maintained by the combined action of several evolutionary forces and that inversions are enriched in odorant receptor genes encoding key 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 is pushing the limits of genomic architecture complexity.