Characterization of intratumoral heterogeneity is critical to cancer therapy, as the presence of phenotypically diverse cell populations commonly fuels relapse and resistance to treatment. Although genetic variation is a well-studied source of intratumoral heterogeneity, the functional impact of most genetic alterations remains unclear. Even less understood is the relative importance of other factors influencing heterogeneity, such as epigenetic state or tumor microenvironment. To investigate the relationship between genetic and transcriptional heterogeneity in a context of cancer progression, we devised a computational approach called HoneyBADGER to identify copy number variation and loss of heterozygosity in individual cells from single-cell RNA-sequencing data. By integrating allele and normalized expression information, HoneyBADGER is able to identify and infer the presence of subclone-specific alterations in individual cells and reconstruct the underlying subclonal architecture. By examining several tumor types, we show that HoneyBADGER is effective at identifying deletions, amplifications, and copy-neutral loss-of-heterozygosity events and is capable of robustly identifying subclonal focal alterations as small as 10 megabases. We further apply HoneyBADGER to analyze single cells from a progressive multiple myeloma patient to identify major genetic subclones that exhibit distinct transcriptional signatures relevant to cancer progression. Other prominent transcriptional subpopulations within these tumors did not line up with the genetic subclonal structure and were likely driven by alternative, nonclonal mechanisms. These results highlight the need for integrative analysis to understand the molecular and phenotypic heterogeneity in cancer.