Lysosomal storage diseases (LSDs) are a heterogeneous group of rare multisystem metabolic disorders occurring mostly in infancy and childhood, characterized by a gradual accumulation of non-degraded substrates inside the cells. Although biochemical enzymatic assays are considered the gold standard for diagnosis of symptomatic patients, genotyping is a requirement for inclusion in enzyme replacement programs and is a prerequisite for carrier tests in relatives and DNA-based prenatal diagnosis. The emerging next-generation sequencing (NGS) technologies are now offering a powerful diagnostic tool for genotyping LSDs patients by providing faster, cheaper, and higher-resolution testing options, and are allowing to unravel, in a single integrated workflow SNVs, small insertions and deletions (indels), as well as major structural variations (SVs) responsible for the pathology. Here, we summarize the current knowledge about the most recurrent and private SVs involving LSDs-related genes, review advantages and drawbacks related to the use of the NGS in the SVs detection, and discuss the challenges to bring this type of analysis in clinical diagnostics.