Next-generation sequencing (NGS) technologies have revolutionised the analysis of genomic structural variants (SVs), providing significant insights into SV de novo formation based on analyses of rearrangement breakpoint junctions. The short DNA reads generated by NGS, however, have also created novel obstacles by biasing the ascertainment of SVs, an aspect that we refer to as the ‘short-read dilemma’. For example, recent studies have found that SVs are often complex, with SV formation generating large numbers of breakpoints in a single event (multi-breakpoint SVs) or structurally polymorphic loci having multiple allelic states (multi-allelic SVs). This complexity may be obscured in short reads, unless the data is analysed and interpreted within its wider genomic context. We discuss how novel approaches will help to overcome the short-read dilemma, and how integration of other sources of information, including the structure of chromatin, may help in the future to deepen the understanding of SV formation processes.