The anatomy of healthy humans shows much minor variation, and twin‐studies reveal at least some of this variation cannot be explained genetically. A plausible explanation is that fine‐scale anatomy is not specified directly in a genetic programme, but emerges from self‐organizing behaviours of cells that, for example, place a new capillary where it happens to be needed to prevent local hypoxia. Self‐organizing behaviour can be identified by manipulating growing tissues (e.g. putting them under a spatial constraint) and observing an adaptive change that conserves the character of the normal tissue while altering its precise anatomy. Self‐organization can be practically useful in tissue engineering but it is limited; generally, it is good for producing realistic small‐scale anatomy but large‐scale features will be missing. This is because self‐organizing organoids miss critical symmetry‐breaking influences present in the embryo: simulating these artificially, for example, with local signal sources, makes anatomy realistic even at large scales. A growing understanding of the mechanisms of self‐organization is now allowing synthetic biologists to take their first tentative steps towards constructing artificial multicellular systems that spontaneously organize themselves into patterns, which may soon be extended into three‐dimensional shapes.