The study of gaseous haloes holds the key to understanding gas flows in and out of galaxies, which in turn determines how galaxies form and evolve.

However, recent observations have revealed them to be very complex, with the presence of significant amounts of multiphase gas, driven by a range of physical process within galaxies as well as by the larger-scale environment. Simulations that realistically model this gas are therefore crucial to interpreting this new data, and ultimately helping us understand how galaxies assemble. However, many cosmological simulations sacrifice resolution in gaseous haloes to reduce their computational cost, meaning their ability to accurately resolve some of the key physical processes, such as turbulence and instabilities, can be limited.

Using cosmological simulations, in this thesis I have investigated how gaseous haloes evolve over time. I have implemented a new shock refinement scheme to boost numerical resolution in gaseous haloes. Applied to a massive cluster progenitor, I found significant increases in cold gas mass in filaments and clumps, leading to more widespread star formation. In the hot halo there is a notable boost in turbulent velocities, leading to a doubling of non-thermal pressure support.

With the FABLE suite, I studied how the hydrostatic mass bias and turbulent pressure support level in galaxy clusters change as they undergo major mergers and are host to powerful feedback episodes. I found that clusters rarely tend to be in hydrostatic equilibrium for long, with variations being driven by both merger activity and interestingly, at higher redshift, AGN feedback. Such insights could be important for future cluster mass estimates from X-ray and SZ observations, for use as cosmological probes.

Finally, I simulated the growth of an ultramassive black hole of mass ∼ 10^10 M⊙ by z = 6. I have studied its impact on the gaseous halo around it, including how powerful AGN feedback can disrupt inflowing cold filaments and increase the thermal pressure of the surrounding gas. I found that strong AGN-driven outflows can deposit significant quantities of metals at very large distances from the central galaxy, which could be a unique signature of the presence of such ultramassive black holes in the very early Universe.

Many of the effects predicted by the simulations described in this thesis have the potential to be observed (or ruled out) in the coming decade or two, with an incoming wealth of observational data from observatories like JWST, Athena, CMB-S4, SKA, and LISA. These data, combined with further developments in theory and simulation, will therefore revolutionise our understanding of gaseous haloes.