Structural variations (SV) are pervasive in plants. Maize displays a huge number of SVs, including Insertion/Deletion (InDel) or Presence/Absence variation (PAV) that lead to differences in gene content between individuals. These structural polymorphisms may contribute to trait variation, adaptation and heterosis by changing and complementing the gene/regulatory regions between individuals. To analyze the effect of InDels/PAVs on trait variation and adaptation, we genotyped 362 inbred lines representing a broad range of diversity with (i) a new Affymetrix® Axiom® array of 105,947 InDels ranging from 35bp to 129,7Kbp and (ii) the 600K SNPs Affymetrix Axiom array and by Genotyping by Sequencing to reach a number of 1 million SNPs. Half of InDels were not in strong linkage disequilibrium (r2>0.8) with any nearby SNPs. Accordingly, Genome wide association studies (GWAS) on 23 agronomic traits identified 13 new quantative trait loci (QTLs) with InDels as compared to 281 detected by SNPs. Genomic regions under selection between tropical, dent and flint lines were enriched in InDels polymorphisms with 56 out 188 genomic regions detected. These InDels/PAVs targeted genes involved in tolerance to biotic and abiotic stress and/or adaptive traits as flowering time. To study the effect of InDels on hybrid performance, we derived 287 hybrids by crossing 210 maize temperate lines from the previous panel and observed their female flowering, plant height and grain yield (GY) in four different environments. We performed GWAS with InDels/PAVs and SNPs and detected 78 and 133 QTLs with respectively an additive or dominance effect, respectively. Six additive and 11 dominant QTLs were exclusively detected by InDels, including one QTL for GY targeting a large cluster of InDels/PAVs on chromosome 6. However, Integrating InDels/PAVs information to estimate kinship to predict hybrid performance using an additive and dominant model did not increase predictive ability.