Structural variants and presence/absence polymorphisms are common in plant genomes, yet they are routinely overlooked in genome-wide association studies (GWAS). Here, we expand the genetic variants detected in GWAS to include major deletions, insertions, and rearrangements. We first use raw sequencing data directly to derive short sequences, k -mers, that mark a broad range of polymorphisms independently of a reference genome. We then link k -mers associated with phenotypes to specific genomic regions. Using this approach, we re-analyzed 2,000 traits measured in Arabidopsis thaliana, tomato , and maize populations. Associations identified with k -mers recapitulate those found with single-nucleotide polymorphisms (SNPs), however, with stronger statistical support. Moreover, we identified new associations with structural variants and with regions missing from reference genomes.Our results demonstrate the power of performing GWAS before linking sequence reads to specific genomic regions, which allow detection of a wider range of genetic variants responsible for phenotypic variation.Here, we present an efficient method for k -mer-based GWAS and compare it directly to the conventional SNP-based approach on more than 2,000 phenotypes from three plant species with different genome and population characteristics -A. thaliana , maize and tomato. Most variants identified by SNPs can be detected with k -mers (and vice versa), but k -mers having stronger statistical support.For k -mer-only hits, we demonstrate how different strategies can be used to infer their genomic context, including large structural variants, sequences missing from the reference genome, and organeller variants. Lastly, we compute population structure directly from k -mers, enabling the analysis of species with poor quality or without a reference genome. In summary, we have inverted the conventional approach of building a genome, using it to find population variants, and only then associating variants with phenotypes. In contrast, we begin by associating sequencing reads with phenotypes, and only then infer the genomic context of these sequences. We posit that this change of order is especially effective in plant species, for which defining the full population-level genetic variation based on reference genomes remains highly challenging. Schneeberger et al., 2009) . While traditional GWAS methods will benefit from these technological improvements, so will k -mer based approaches, which will be able to use tags spanning larger genomic distances. Therefore, we posit that for GWAS purposes, k -mer based approaches are ideal because they minimize arbitrary choices when classifying alleles and because they capture more, almost optimal, information from raw sequencing data. 578