People play a central role in the machine learning life cycle. Consequently, building machine learning systems that are reliable, trustworthy, and fair requires that relevant stakeholders—including developers, users, and the people affected by these systems—have at least a basic understanding of how they work. Yet what makes a system “intelligible” is difficult to pin down. Intelligibility is a fundamentally human-centered concept that lacks a one-size-fits-all solution. I will explore the importance of evaluating methods for achieving intelligibility in context with relevant stakeholders, ways of empirically testing whether intelligibility techniques achieve their goals, and why we should expand our concept of intelligibility beyond machine learning models to other aspects of machine learning systems, such as datasets and performance metrics.