The ability to generate 3-dimensional models of the developing human kidney via the directed differentiation of pluripotent stem cells—termed kidney organoids—has been hailed as a major advance in experimental nephrology. Although these provide an opportunity to interrogate human development, model-specific kidney diseases facilitate drug screening and even deliver bioengineered tissue; most of these prophetic end points remain to be realized. Indeed, at present we are still finding out what we can learn and what we cannot learn from this approach. In this review, we will summarize the approaches available to generate models of the human kidney from stem cells, the existing successful applications of kidney organoids, their limitations, and remaining challenges.