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 conclude that X-ray coronae are radiatively-compact and have electron temperatures regulated by electron-positron pair production. We show that the predominance of rapidly-rotating objects in current surveys of SMBH spin is entirely unsurprising once one accounts for the observational selection bias resulting from the spin-dependence of the radiative efficiency. We review recent progress in our understanding of fast (v~0.1-0.3c), highly-ionized (mainly visible in FeXXV and FeXXVI lines), high-column density winds that may dominate quasar-mode galactic feedback. Finally, we end with a brief look forward to the promise of Astro-H and future X-ray spectropolarimeters.
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