Spurred by the observational breakthroughs made by the Event Horizon Telescope collaboration, we have developed new theoretical tools for understanding the effects of general relativity on the appearance of sources near Kerr black holes. Among these are a complete analytical solution of the null geodesic equation, the sharpening of “shadow” and “photon ring” heuristics, and an accounting of the properties of multiple images in terms of universal exponents. I will discuss the basics of interpreting horizon-scale images, with the aim of disentangling properties of the black hole spacetime from the details of the astrophysical source. I will argue that present observations cannot cleanly separate the two, but will show that general relativity provides a rich structure that may be observable in the future.