Organoids, self-organizing 3D structures created from a variety of cell sources, offer unique advantages for studying organ development, modeling diseases, discovering new drugs, and creating regenerative therapies. However, their ability to completely mimic complex in vivo organ structure and function has been hindered by the lack of all relevant cell types found in each organ; heterogeneity of cell types between organoids; variable reproducibility; lack of a mature phenotype; and lack of integrated neural, vascular, and hematopoietic networks. To address these critical challenges, various strategies are being rapidly advanced and include co-culturing and co-differentiating multiple cell types to create organoids; co-culturing region-and lineage-specific organoids together, including with vascular organoids, to create assembloids; using organoid-on-a-chip technology to integrate perfusable vasculature within organoids; and using 3D bioprinting to create complex and perfusable organoids. This brief overview explores how the converging disciplines of stem cell biology, developmental biology, and advanced bioengineering technologies have progressed the creation of increasingly sophisticated organoid models, and provides an outlook on how remaining challenges might be addressed.