This thesis examines the AGN - star formation relation in galaxies out to z=4, probing the interplay between these two phenomena at various redshifts, for different galaxy morphologies, and at different luminosities.

We have created a catalogue of 12,000 local infrared galaxies with optical morphological classifications, BPT analysis, and physical parameters derived from SED fits. We explore the variation in specific SFR and AGN fraction with morphology, compare star formation rate estimators, and provide a morphological breakdown of the IR luminosity distribution.

Focusing on the Spirals and Barred Spirals from the M-IIFSCz, we find their distributions of specific star formation rates are statistically consistent. Conversely, Barred Spirals have a significantly higher AGN fraction than non-barred Spirals at both high and low stellar masses, but if we control for g-r colour, the AGN fraction is independent of bar presence. We discuss the implications of this result.

We perform spectroscopic follow-up of 46 galaxies identified in the IIFSCz as ULIRGs and HLIRGs through photometric redshifts. By deriving spectroscopic redshifts, we show that their photometric redshifts are overestimated by an average factor of zphot/zspec=1.7. We quantify the implications for the Luminosity Function and show that applying a general correction for photometric redshift over-
estimation reduces the number density of HLIRGs by 75%.

At 1<z<4, we study 35 QSOs and find that rapid accretion is occuring onto relatively low-mass black holes. Their SFR:accretion rate ratios average 100:1; considerably lower than the typical value of 1000:1 seen in low-to-medium luminosity AGN in the local Universe, potentially due to star formation suppression.