The coeval AGN and galaxy evolution and the observed local relations between super-massive black holes (SMBHs) and galaxy properties suggest some connection or feedback between SMBH growth and galaxy build-up. The authors looked for correlations between properties of X-ray detected AGN and their far-infrared (FIR) detected host galaxies, to find quantitative evidences for this connection, highly debated in recent years. They exploit the rich multi-wavelength data set (from X-ray to FIR) that is available in the COSMOS field for a large sample (692 sources) of AGN and their hosts, in the redshift range 0.1 < z < 4, and use X-ray data to select AGN and determine their properties (intrinsic luminosity and nuclear obscuration), and broad-band (from UV to FIR) spectral energy distribution (SED) fitting to derive host galaxy properties, viz., the stellar mass (M<sub>*</sub>) and the star formation rate (SFR). The authors find that the AGN 2-10 keV luminosity (L<sub>X</sub>) and the host galaxy 8-1000 um star formation luminosity (L<sup>SF</sup><sub>IR</sub>) are significantly correlated. However, the average host L<sup>SF</sup><sub>IR</sub> has a flat distribution in bins of AGN L<sub>X</sub>, while the average AGN L<sub>X</sub> increases in bins of host L<sup>SF</sup><sub>IR</sub>, with a logarithmic slope of ~ 0.7, in the redshifts range 0.4 < z < 1.2. In the reference paper, the authors also discuss the comparison between the distribution of these two quantities and the predictions from hydrodynamical simulations. Finally, they find that the average column density (N<sub>H</sub>) shows a positive correlation with the host M<sub>*</sub>, at all redshifts, but not with the SFR (or L<sup>SF</sup><sub>IR</sub>). This translates into a negative correlation with specific SFR. These results are in agreement with the idea that BH accretion and SFRs are correlated, but occur with different variability time scales. The presence of a positive correlation between N<sub>H</sub> and host M<sub>*</sub> suggests that the X-ray N<sub>H</sub> is not entirely due to the circumnuclear obscuring torus, but may also include a contribution from the host galaxy. This table summarizes the multiwavelength properties of the 692 AGN-host systems detected in the COSMOS field both in the X-ray and in the FIR (the X-FIR sample). This table was created by the HEASARC in July 2017, based on <a href="https://cdsarc.cds.unistra.fr/ftp/cats/J/A+A/602/A123">CDS Catalog J/A+A/602/A123</a> file table1.dat, which contains the multiwavelength properties of the 692 sources in the X-FIR sample. This is a service provided by NASA HEASARC .