Several scenarios have been proposed to describe the physical connection between galaxies and their central active galactic nuclei (AGN). This connection could act on a range of spatial scales and vary across cosmic time. In these proceedings, we consider black hole and galaxy growth and whether that growth is affected by AGN feedback both based on statistical approaches – which reveal general population trends – and based on an individual case study – which gives us a more detailed insight on the physical processes at play. For the statistical approach, we showcase a low-redshift (0.04 < z < 0.2) SDSS sample with AGN classification based on a combination of emission-line diagnostic diagrams, and for which we account for sample selection by using a V/Vmax approach. The trends on the star formation rate - stellar mass (SFR – M*) plane suggest that the most likely connection is a common gas reservoir for star formation and AGN, and that they both decline as the gas reservoir is consumed. The trends established at low-redshift could act as a local benchmark against which to compare higher redshift studies. As a complementary approach, we use a detailed case study of a nearby AGN host with integral field spectroscopy from the VLT/MUSE instrument in order to spatially resolve the interplay between AGN feedback and the host galaxy. We find that the galaxy substructure likely plays a role by collimating and/or obscuring the outflows and radiation from the central engine. Ongoing and future work with 3D spectroscopy will enable us to learn more about galaxy and black hole coevolution. Lastly, we briefly discuss lessons learnt from both approaches.

NGC 7582 was identified as a starburst galaxy in the optical (Veron et al. 1981) but its X-ray emission is typical of a Seyfert 1 galaxy (Ward et al. 1978). We analyzed a datacube on this object obtained with the GMOS-IFU on the Gemini-South telescope. After a subtraction of the stellar component using the starlight code (Cid Fernandes et al. 2005), we looked for optical signatures of the AGN. We detected a broad Hα component (Figure 1) in the source where Bianchi et al. (2007) identified the AGN in an HST optical image. We also found a broad Hβ feature (Figure 2), but its emission reveals a extended source. We suggest that it is the light of the AGN scattered in the ionization cone. We propose that NGC 7582 is a Seyfert 1 galaxy. A number of other “hot-spots” and Wolf–Rayet features were also identified.