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Genetic diversity and population structure are key resources for breeding purposes and genetic studies of important agronomic traits in crops. In this study, we described SNP-based genetic diversity, linkage disequilibrium and population structure in a panel of 179 bread wheat advanced cultivars and old accessions from Bulgaria, using an optimized wheat 25K Infinium iSelect array. Out of 19,019 polymorphic SNPs, 17,968 had а known chromosome position on the A (41%), B (42%) and D (11%) genome, and 6% were not assigned to any chromosome. Homoeologous group 4, in particular chromosome 4D, was the least polymorphic. In the total population, the Nei’s gene diversity was within the range 0.1-0.5, and the polymorphism information content ranged from 0.1 to 0.4. Significant differences between the old and modern collections were revealed with respect to the linkage disequilibrium (LD): the average values for LD (r2), the percentage of the locus pairs in LD and the LD decay were 0.64, 16% and 3.3 for the old germplasm, and 0.43, 30% and 4.1 for the modern releases, respectively. Structure and k-means clustering algorithm divided the panel into three groups. The old accessions formed a distinct subpopulation. The cluster analysis further distinguished the modern releases according to the geographic region and genealogy. Gene exchange was evidenced mainly between the subpopulations of contemporary cultivars. The achieved understanding of the genetic diversity and structure of the Bulgarian wheat population and distinctiveness of the old germplasm could be of interest for breeders developing cultivars with improved characteristics. The obtained knowledge about SNP informativeness and the LD estimation are worthwhile for selecting markers and for considering the composition of a population in association mapping studies of traits of interest.