Over the past decade, genome-wide assays for chromatin interactions in single cells have enabled the study of individual nuclei at unprecedented resolution and throughput. Current chromosome conformation capture techniques survey contacts for up to tens of thousands of individual cells, improving our understanding of genome function in 3D. However, these methods recover a small fraction of all contacts in single cells, requiring specialised processing of sparse interactome data. In this review, we highlight recent advances in methods for the interpretation of single-cell genomic contacts. After discussing the strengths and limitations of these methods, we outline frontiers for future development in this rapidly moving field.