The buildup of stellar and black hole mass peaked during z=1-3. Infrared (IR) luminous galaxies, which are massive and heavily dust obscured (LIR > 1011 Lsun), dominate the stellar growth during this era, and many are harboring a hidden active galactic nucleus (AGN). We have quantified the contribution of AGN heating to the infrared emission of a large sample of dusty, luminous galaxies from z=0.5-4 using Spitzer mid-IR spectroscopy, available for every source. We classify sources as star forming galaxies, AGN, or composites based on the presence of mid-IR continuum emission due to a dusty torus. 60% of our sample shows signs of some dust heating emanating from an AGN, and that an AGN is clearly linked with increasing dust temperatures. We quantify the far-IR emission using deep Herschel imaging and find that the strength of mid-IR AGN emission is tightly correlated with the total contribution of an AGN to LIR, which has important consequences for calculating star formation rates in dusty high redshift galaxies. We calibrate techniques to remove the contribution of AGN to LIR. Because of dust obscuration, much of this AGN activity is undetected at other wavelengths, but we present new color diagnostics to effectively identify heavily obscured AGN. We discuss the role that mergers might play in fueling AGN growth and find our galaxies to be generally consistent with the picture that a major merger triggers an AGN. We test what effect an IR luminous AGN has on the star formation efficiency (the star formation rate compared with the molecular gas mass) using a pilot sample of 24 galaxies at z