Measuring the spins of supermassive black holes (SMBHs) in active galactic nuclei (AGN) can inform us about the relative role of gas accretion vs. mergers in recent epochs of the life of the host galaxy and its AGN. Recent advances in theory and observation have enabled spin measurements for a handful of SMBHs thus far, but this science is still very much in its infancy. Herein, I discuss how and why we seek to measure black hole spin in AGN, using recent results from long X-ray observing campaigns on three radio-quiet AGN (MCG-6-30-15, NGC 3783 and Fairall 9) to illustrate this process and its caveats. I then present our current knowledge of the distribution of SMBH spins in the local universe. I also address prospects for improving the accuracy, precision and quantity of these spin constraints in the next decade and beyond with instruments such as NuSTAR, Astro-H and a future generation large-area X-ray telescope.