Chromosomal rearrangements are a source of structural variation within the genome that figure prominently in human disease, where the importance of translocations and deletions is well recognized. In principle, inversions—reversals in the orientation of DNA sequences within a chromosome—should have similar detrimental potential. However, the study of inversions has been hampered by traditional approaches used for their detection, which are not particularly robust. Even with significant advances in whole genome approaches, changes in the absolute orientation of DNA remain difficult to detect routinely. Consequently, our understanding of inversions is still surprisingly limited, as is our appreciation for their frequency and involvement in human disease. Here, we introduce the directional genomic hybridization methodology of chromatid painting—a whole new way of looking at structural features of the genome—that can be employed with high resolution on a cell-by-cell basis, and demonstrate its basic capabilities for genome-wide discovery and targeted detection of inversions. Bioinformatics enabled development of sequence- and strand-specific directional probe sets, which when coupled with single-stranded hybridization, greatly improved the resolution and ease of inversion detection. We highlight examples of the far-ranging applicability of this cytogenomics-based approach, which include confirmation of the alignment of the human genome database and evidence that individuals themselves share similar sequence directionality, as well as use in comparative and evolutionary studies for any species whose genome has been sequenced. In addition to applications related to basic mechanistic studies, the information obtainable with strand-specific hybridization strategies may ultimately enable novel gene discovery, thereby benefitting the diagnosis and treatment of a variety of human disease states and disorders including cancer, autism, and idiopathic infertility.Electronic supplementary materialThe online version of this article (doi:10.1007/s10577-013-9345-0) contains supplementary material, which is available to authorized users.