Organoids are simple tissue-engineered cell-based in vitro models that recapitulate many aspects of the complex structure and function of the corresponding in vivo tissue. They can be dissected and interrogated for fundamental mechanistic studies on development, regeneration and repair in human tissues, and can also be used in diagnostics, disease modelling, drug discovery and personalized medicine. Organoids are derived from either pluripotent or tissue-resident stem (embryonic or adult) or progenitor or differentiated cells from healthy or diseased tissues, such as tumours. To date, numerous organoid engineering strategies that support organoid culture and growth, proliferation, differentiation and maturation have been reported. This Primer highlights the rationale underlying the selection and development of these materials and methods to control the cellular/tissue niche; and therefore, the structure and function of the engineered organoid. We also discuss key considerations for generating robust organoids, such as those related to cell isolation and seeding, matrix and soluble factor selection, physical cues and integration. The general standards for data quality, reproducibility and deposition within the organoid community are also outlined. Lastly, we conclude by elaborating on the limitations of organoids in different applications, and the key priorities in organoid engineering for the coming years.