Post-starburst (PSB) galaxies are the galaxies in which star formation has recently been sharply truncated, as indicated by strong Balmer absorption lines alongside weak or absent nebular emission lines. PSBs are believed to be an important transitional state between the star- forming and quiescent populations, and could be important candidates for the “fast” quenching route. From observations alone, it is challenging to figure out what mechanisms produce PSBs and how important PSBs are to the growth of the red sequence. Combining simulations and observations is one of the most important methodologies to answers these questions. In this thesis, I run a set of binary merger simulations, with a variety of black hole feedback models, progenitor galaxies, orbits and mass ratios, to reproduce PSBs. I find that only major mergers on prograde-prograde or retrograde-prograde orbits in combination with a mechanical black hole feedback model can form galaxies that can be selected by the traditional PSB selection method. The difficulty in reproducing the very young PSBs in simulations potentially indicates that new sub-resolution star formation recipes are required to properly model the process of star formation quenching. I develop the SEDmorph code to create mock datacubes of the simulated galaxies, in order to investigate the radial gradients in the spectral indices of PSBs. In my simulations, I find the gradients are caused by the fact that the starburst peaks at the same time at all radii, but is stronger and more prolonged in the inner regions. To find out the contribution of the fast quenching route to the growth of the red sequence, I study the population of rapidly quenched galaxies (RQGs) in the SIMBA cosmological hydro- dynamic simulation at 0.5 < z < 2, comparing directly to observational PSBs in the UKIDSS Ultra Deep Survey via their colour distributions and mass functions. I find that the fraction of quiescent galaxies that are rapidly quenched in SIMBA is 59% (or 48% in terms of stellar mass), which is higher than observed. A similar “downsizing” of RQGs is observed in both SIMBA and the UDS, with RQGs at higher redshift having a higher average mass. However, SIMBA pro- duces too many RQGs at 1 < zq < 1.5 and too few low mass RQGs at 0.5 < zq < 1. SIMBA also shows various inconsistencies in star formation and chemical enrichment histories, including an absence of short, intense starbursts. These results will help inform the next generation of galaxy evolution models, particularly with respect to the quenching mechanisms employed.