The concept of cell type is key for modeling biology. Recent technological advances are prompting us to rethink what we understand by cell type and how we classify them. There is currently no consensus for a definition of cell type, which makes it hard to integrate knowledge across life sciences. We propose here that a cell type should represent any class of cell that (1) is explicitly defined; (2) is identifiable within a taxon; and (3) is theoretically useful. We also present four classes of cell types: sensu stricto cell types, archetypes, infratypes, and technotypes. They respectively specify cell type concepts applied to a single species, multiple species, populations below the species level, and particular experiments. The flexible and rigorous framework we propose can base annotation of single-cell omics datasets, and reconcile knowledge about cells across all different domains of science.