Leaf rust, caused by Puccinia triticina Erikss. (Pt), and stem rust, caused by Puccinia graminis f. sp. tritici Erikss. and E. Henn (Pgt), are among the most devastating diseases of durum wheat (Triticum turgidum L. var. durum). This study focused on the identification of Lr and Sr loci using association mapping (AM) and bi-parental population mapping. From the AM conducted on the USDA-National Small Grain Collection (NSGC), 37 loci associated with leaf rust response were identified, of which 14 were previously uncharacterized. Inheritance study and bulked segregant analysis on bi-parental populations developed from eight leaf rust resistance accessions from the USDA-NSGC showed that five of these accessions carry single dominant Lr genes on chromosomes 2B, 4A, 6BS, and 6BL. The other three accessions have Lr genes with more complex inheritance. All eight accessions carry different genes than those already mapped in durum cultivars except one accession with Lr61. Linkage mapping in two of the bi-parental populations showed that the gene in PI 209274 (LrCA) was mapped to 6BS between SNPs IWA3298 and IWB39456, while the gene in PI 192051 (LrPort) was mapped to 4AL, flanked by IWA4254 and IWA8341. Resistance to Pgt-race TTKSK was also observed in PI 534304 and PI 192051. PI 534304 was found to carry Sr13 on chromosome 6AL, while PI 192051 carries a novel Sr gene (SrPort) mapped to 7AS flanked by IW8390 and IWA1805. The genotype PI 192051 has an additional QTL (QSr.ndsu-5B) to Pgt races in a field trial in Ethiopia in 2016. The QSr.ndsu-5B was mapped to 5BL and delimited by IWA6992 and IWA2181. The study of virulence diversity in Pt isolates collected from several countries identified seven races among 51 isolates collected from durum wheat and 21 races among 40 isolates collected from common wheat. The phylogeny study on 30 Pt isolates based on the Restriction-Associated DNA (RAD)-Genotype by Sequencing (GBS), clustered the isolates into eight clades, with higher diversity in the SNP genotypes in common wheat isolates compared to that in durum wheat isolates. RAD-GBS is identified as a suitable and informative genotyping technique to study the population genetics of Pt.