In recent years considerable progress has been made in the development of faithful procedures for the differentiation of human pluripotent stem cells (hPSCs). An important step in this direction has also been the derivation of organoids. This technology generally relies on traditional three-dimensional culture techniques that exploit cell-autonomous self-organization responses of hPSCs with minimal control over the external inputs supplied to the system. The convergence of stem cell biology and bioengineering offers the possibility to provide these stimuli in a controlled fashion, resulting in the development of naturally inspired approaches to overcome major limitations of this nascent technology. Based on the current developments, we emphasize the achievements and ongoing challenges of bringing together hPSC organoid differentiation, bioengineering and ethics. This Review underlines the need for providing engineering solutions to gain control of self-organization and functionality of hPSC-derived organoids. We expect that this knowledge will guide the community to generate higher-grade hPSC-derived organoids for further applications in developmental biology, drug screening, disease modelling and personalized medicine.