In this talk, I will review the recent progress on the correlations between AGN and their host galaxies. Specifically, we studied the relationship between AGN and star formation in a sample of infrared AGNs, and compared several AGN SED models and the effect of AGN removal in the infrared based on their X-ray information. We found significant AGN contributions to the infrared luminosities and corresponding star formation rate estimates. I will then review the AGN-star formation relation on a multi-parameter space and how different parameters and sample selectionsaffect the observed correlation. Finally, I will report our recent progress on the constant ratio between the star formation rate and the black hole mass accretion rate, and their implications on the gas supply, galaxy formation history, and galaxy evolutionary models.