Single-cell multi-omics has recently emerged as a powerful technology by which different layers of genomic output—and hence cell identity and function—can be recorded simultaneously. Integrating various components of the epigenome into multi-omics measurements allows for studying cellular heterogeneity at different time scales and for discovering new layers of molecular connectivity between the genome and its functional output. Measurements that are increasingly available range from those that identify transcription factor occupancy and initiation of transcription to long-lasting and heritable epigenetic marks such as DNA methylation. Together with techniques in which cell lineage is recorded, this multilayered information will provide insights into a cell's past history and its future potential. This will allow new levels of understanding of cell fate decisions, identity, and function in normal development, physiology, and disease.