The Milky Way is only one of the billions of galaxies in the Universe and in many aspects it can be considered a typical one. At the centre, a supermassive black hole can be found, with a mass about 4 million times that of the Sun. The region of influence of the supermassive black hole is small compared to the host galaxy, so only material extremely close to the black hole is expected to fall in. When large amounts of matter do fall into such a supermassive black hole, the amount of energy released can be colossal. Matter heats up as it falls in, radiates thermally and eventually the temperature is so high that electrons and protons are separated to form a plasma. Magnetic fields accelerate these particles to almost the speed of light, causing them to radiate further. Growing supermassive black holes, known as active galactic nuclei (AGN), release this energy through different forms of radiation, which reflect the different physical processes going on. This information can be used to inferr properties such as the mass of the black hole, the amount of matter falling in, and the strength of the magnetic fields. Not all AGN show the same types of radiation, and depending on the wavelength of light that one uses to look for them, AGN with different properties are found. Some of these differences are real, in the sense that the AGN are emitting with different intensities at different wavelengths, but sometimes the difference is only apparent. For example, gas and dust around the infalling matter or in the host galaxy can block our line of sight, so that some of the radiation is hidden. The dust hides mainly the optical and ultraviolet radiation, so that using infrared or radio telescopes allows one to find these obscured AGN. The overall aim of this project is to understand the population of growing supermassive black holes and their host galaxies, and this requires a complete census of AGN as well as an understanding of the physical processes. The approach will be through three main objectives. The first of these is to accurately quantify the population of hidden AGN and their evolution, for which the census is still incomplete. The energy emitted by this hidden population needs to be taken into account accurately, to understand how the growth of supermassive black holes occurs. For example, comparison of the total amount of energy radiated by all AGN to the density of dormant supermassive black holes gives us information on what fraction of the infalling mass was radiated away and did not reach the black hole, but this calculation must include the hidden AGN too. Current research suggests that the most complete method of finding obscured AGN is by looking for them at mid-infrared wavelengths, however, galaxies without an AGN can sometimes also emit strongly in the mid-infrared. Therefore we will use the complete spectrum between ultraviolet and mid-infrared, using a technique I developed, to identify the AGN and separate them from the non-AGN contaminants. The second objective is to use the observed properties of AGN to constrain the physical properties of the supermassive black holes. Many of these are believed to be understood but not all. For example the reason why only some AGN have powerful radio emission is still a matter of debate, with the most promising explanation being the spin of the black hole. Understanding the information that radio emission gives us will then allow us to use the next generation of radio telescopes to study these properties growing black holes, for example what is the mass, the spin and how much matter is it consuming. Finally, I will study the interaction of the host galaxy with the AGN. It seems that some of the AGN are obscured by young, dusty galaxies, which might still be forming. I will also study the star formation in the host galaxies. Thus, I will study, in parallel, the growth of the supermassive black hole and host galaxy, and how these are related.