Modern far-infrared and sub-millimetre observatories have opened our eyes to the cold dusty Universe. They provide arguably the best tracers for star-formation in active galactic nuclei (AGN), since luminous nuclear activity is inefficient at keeping dust cold. I will report on studies that bring together modern multi-wavelength surveys, including those from Herschel and ALMA, towards developing a coherent view of the growth of supermassive black holes (in AGN) in relation to the growth of galaxies (through star-formation). Weak or stochastic co-evolution plays a paramount role, driven by the smooth increase of gas content in massive galaxies over time rather than short, intense episodes such as star-bursts or mergers. I will discuss the game-changing value of ALMA: allowing us to individually measure weak star-formation in distant galaxies, and define the scope of AGN feedback and its likely role in galaxy evolution.