Galaxy evolution is still relatively poorly understood. Specifically, star formation, mergers and the influence of a central supermassive black hole are all thought to be key drivers in regulating galaxy formation and evolution, but their relative contributions are not well constrained. Velocity dispersion (σ), a measure of the statistical variance of stellar motions in a galaxy, is known to be a key galaxy property, effectively tracing a galaxy's gravitational potential well. The evolution of σ with cosmic time is also not well understood, despite having the potential to shed light on the relative importance of mergers versus star formation in building galaxies. σ is also known to be closely connected to the mass of the central supermassive black hole, via a tight correlation with slope of ∼ 4−6, which theories suggest could be a result of energetic winds/jets from active galactic nuclei (AGN) impacting onto the surrounding interstellar medium. In this work, I present a comprehensive semi-empirical approach to compute σ via detailed Jeans modelling, assuming, for the first time, both a constant and scale-dependent mass-to-light ratio M∗/L. I compare with a large sample of local galaxies from the MaNGA survey and find that both models can reproduce the Faber-Jackson relation and the weak dependence of σ with bulge-to-total ratio. I also explore the dynamical-to-stellar mass ratio within R ≲ Re , and show that the full dynamical mass within the effective radius can be fully accounted for by a gradient in M∗/L or a dark matter halo with an NFW profile. I then build velocity dispersion evolutionary histories, using the average histories of main progenitor dark matter haloes, assigning stellar masses, effective radii and Sersic indices via a variety of abundance matching, and empirically motivated relations. I find clear evidence for downsizing in velocity dispersion histories along the progenitor tracks, and a steady increase in velocity dispersion at fixed stellar mass with increasing redshift. I extract comparable velocity dispersion tracks from the TNG50 hydrodynamic simulation. The relative 'flatness' of these tracks is shown to be driven by the increasing dark matter fraction within Re, whilst showing a steeper evolution in the presence of a stellar gradient. I then show that a combination of mergers and internal star formation are likely responsible for the constant or increasing σap[M∗,z] with time. I then present new evidence for the fundamental nature of the relationship between black hole mass and σ, and show that my σ ap[M∗, z] tracks are consistent with a nearly constant and steep Mbh − σ relation at z ≲ 2, as predicted by AGN feedback models, with black hole masses derived from the LX − M∗ relation. I also show that AGN clustering can place new constraints on black hole-galaxy scaling relations, and explore the creation of AGN mock catalogs. Finally, I present an outcome of these mock catalogs, Astera, my cosmological visualization tool, which presents a real-time rendering of the large scale universe. Astera can represent an invaluable tool for survey planning and, due to its high user interactivity, also for gaming and educational and outreach activities.