Measuring the spin distribution of supermassive black holes is of critical importance for understanding how these black holes and their host galaxies form and evolve over time, yet this type of study is only in its infancy. This brief describes how astronomers measure spin in supermassive black holes using X-ray spectroscopy. It also reviews the constraints that have been placed on the spin distribution in local, bright active galaxies over the past six years, and the cosmological implications of these constraints. Finally, it summarizes the open questions that remain in this exciting new field of research and points toward future discoveries soon to be made by the next generation of space-based observatories.