Recent advances allow access to human cell-based intestinal organoids that recreate human physiology to levels not possible with conventional 2D cell cultures. Despite their huge potential, there are many challenges that remain. This review will cover recent bioengineering approaches to improve organoid maturation, scale up, reproducibility and analysis. The first section covers the advances in engineering the culture environment, followed by the section on tools for micro-manipulation and analysis of organoids. The last section reviews the computational models developed to guide the use of engineered materials and tools, and to interpret observed results as well. The ability to use organoids for discovery research, and the need to both exert exquisite experimental control and obtain quantitative measurements from organoid models means that the field is ripe for collaborative efforts between biologists, engineers, clinicians and industry.