Single-cell genomics has now made it possible to create a comprehensive atlas of human cells. At the same time, it has reopened definitions of a cell’s identity and type and of the ways in which they are regulated by the cell’s molecular circuitry. Emerging computational analysis methods, especially in single-cell RNA sequencing (scRNA-seq), have already begun to reveal, in a data-driven way, the diverse simultaneous facets of a cell’s identity, from a taxonomy of discrete cell types to continuous dynamic transitions and spatial locations. These developments will eventually allow a cell to be represented as a superposition of ‘basis vectors’, each determining a different (but possibly dependent) aspect of cellular organization and function. However, computational methods must also overcome considerable challenges—from handling technical noise and data scale to forming new abstractions of biology. As the scale of single-cell experiments continues to increase, new computational approaches will be essential for constructing and characterizing a reference map of cell identities.