Crop wild relatives represent valuable sources of alleles for crop improvement, including adaptation to climate change and emerging diseases. However, introgressions from wild relatives might have deleterious effects on desirable traits, including yield, due to linkage drag. Here, we analyzed the genomic and phenotypic impacts of wild introgressions in inbred lines of cultivated sunflower to estimate the impacts of linkage drag. First, we generated reference sequences for seven cultivated and one wild sunflower genotype, as well as improved assemblies for two additional cultivars. Next, relying on previously generated sequences from wild donor species, we identified introgressions in the cultivated reference sequences, as well as the sequence and structural variants they contain. We then used a ridge-regression best linear unbiased prediction (BLUP) model to test the effects of the introgressions on phenotypic traits in the cultivated sunflower association mapping population. We found that introgression has introduced substantial sequence and structural variation into the cultivated sunflower gene pool, including >3,000 new genes. While introgressions reduced genetic load at protein-coding sequences, they mostly had negative impacts on yield and quality traits. Introgressions found at high frequency in the cultivated gene pool had larger effects than low-frequency introgressions, suggesting that the former likely were targeted by artificial selection. Also, introgressions from more distantly related species were more likely to be maladaptive than those from the wild progenitor of cultivated sunflower. Thus, breeding efforts should focus, as far as possible, on closely related and fully compatible wild relatives.