Active galactic nuclei (AGN) are complex phenomena. At the heart of an AGN is a relativistic accretion disk around a spinning supermassive black hole (SMBH) with an X-ray emitting corona and, sometimes, a relativistic jet. On larger scales, the outer accretion disk and molecular torus act as the reservoirs of gas for the continuing AGN activity. And on all scales from the black hole outwards, powerful winds are seen that probably affect the evolution of the host galaxy as well as regulate the feeding of the AGN itself. In this review article, we discuss how X-ray spectroscopy can be used to study each of these components. We highlight how recent measurements of the high-energy cutoff in the X-ray continuum by NuSTAR are pushing us to conclu...