Technical progress in materials science and bioprinting has for the past few decades fostered considerable advances in medicine. More recently, the understanding of the processes of self-organization of cells into three-dimensional multicellular structures and the study of organoids have opened new perspectives for tissue engineering. Here, we review microengineering approaches for building functional tissues, and discuss recent progress in the understanding of morphogenetic processes and in the ability to steer them in vitro. On the basis of biological and technical considerations, we emphasize the achievements and remaining challenges of bringing together microengineering and morphogenesis. Our viewpoint underlines the importance of cellular self-organization for the success of tissue engineering in therapeutic applications. We reason that directed self-organization, at the convergence of microengineering and cellular self-organization, is a promising direction for the manufacturing of complex functional tissues.