Single-cell technologies have revolutionized biomedical research by enabling scalable measurement of the genome, transcriptome, proteome, and epigenome of multiple systems at single-cell resolution. Now widely applied to cancer models, these assays offer new insights into tumour heterogeneity, which underlies cancer initiation, progression, and relapse. However, the large quantities of high-dimensional, noisy data produced by single-cell assays can complicate data analysis, obscuring biological signals with technical artifacts. In this review article, we outline the major challenges in analyzing single-cell cancer genomics data and survey the current computational tools available to tackle these. We further outline unsolved problems that we consider major opportunities for future methods development to help interpret the vast quantities of data being generated.