Understanding the causes and potential mitigations of light pollution requires measuring and monitoring artificial light at night (ALAN). We review how ALAN is measured, both from the ground and through remote sensing by satellites in Earth orbit. A variety of techniques are described, including single-channel photometers, all-sky cameras, and drones. Spectroscopic differences between light sources can be used to determine which are most responsible for light pollution, but they complicate the interpretation of photometric data. The variability of Earth's atmosphere leads to difficulty in comparisons between datasets. Theoretical models provide complementary information to calibrate experiments and interpret their results. Here, we identify several shortcomings and challenges in current approaches to measuring light pollution and suggest ways forward.