The 1000 Genomes Project considered structural variation (longer than 50bp in length) based on short read Illumina data in the publication by Sudmant et al. in 2015.
Structural variants are also considred in analysis of high-coverage short read data in work done by NYGC.
However, short read data has limitations for assessing structural variation. The Human Genome Structural Variation Consortium (HGSVC) applied a variety of technologies to explore their abilty to detect structural variation. This work has subsequently been expanded and other projects are using a variety of technologies to produce haplotype resolved genome assemblies.