*Please note this colloquium starts at 4:30 p.m.* The quantum Hall effect, discovered 35 years ago, is a bizarre phenomenon in which a 2D gapped system can nevertheless carry a current. Moreover, the transverse conductivity of the system is precisely quantized in units of e^2/h. Unfortunately, this behavior requires a strong perpendicular magnetic field, and has only been observed at low temperatures. Work of Haldane in 1988 raised the possibility that similar physics could be observed in two-dimensional magnetic systems without any external magnetic field, and potentially at much higher temperatures. Such a system is known as a “quantum anomalous Hall” (QAH) or “Chern” insulator. In this talk I will introduce the essential physics of the QAH effect, provide a tutorial on its mathematical description in terms of Berry phases, and briefly describe recent successes in finding low-temperature realizations. I will then review some of our own recent work in which we propose the deposition of atoms with strong spin-orbit interactions onto the surfaces of magnetic insulators as a promising route toward the synthesis of higher-temperature QAH systems.