Several popular techniques exist for cosmological modelling of galaxies, from computationally intensive hydrodynamical simulations, ab-initio semi-analytic models, to datadriven semi-empirical models. Each has caveats that limit the range of predictions they can make. In hydrodynamical (sub-grid) and semi-analytic models, the high parametrisation can cause degeneracies that prevent clear analysis of which processes are driving galaxy evolution. Furthermore, all must balance simulating a large universe against simulating galaxies with high fidelity. This trade-off between volume and resolution introduces a bias in the number of objects simulated at different masses given differences in cosmological abundances. This thesis describes the STatistical sEmi-Empirical model, steel, and its contributions to the modelling of galaxies. steel is built to overcome the limitations of volume and resolution. We remove these constraints and biases using a novel technique to replace discrete haloes with a statistical alternative. This statistical dark matter backbone is then combined with empirical techniques, e.g. Abundance Matching, to create steel. In this thesis, we use steel to empirically generate robust assembly histories of galaxies, constrained using SDSS and high redshift cluster observations. Using these constraints we probe the in-situ vs. ex-situ growth of galaxies. It is found that within ΛCDM hierarchical assembly using certain stellar mass functions to populate haloes produces a satellite accretion history that is inconsistent with the central galaxy growth. Furthermore, there is a noted tension in the observed galaxy pair fraction and its evolution with redshift. We use the flexible nature of steel we present a systematic investigation into how stellar mass function derivations affect the pair fraction. It is found that the pair fraction can be substantially altered by the type of stellar mass estimates, providing an avenue to remove the discrepancies in pair fraction observations. Finally, there is still an active debate over the significance of mergers on the morphological evolution of galaxies. We find that mergers are capable of creating the observed elliptical fractions and, additionally, a two-pathway merger and in-situ disk instability can produce the observed lenticular fractions. In summary, the STatistical sEmi-Empirical modeL, steel is a new take on galaxy modelling. In this thesis steel has been used to add constraints to galaxy assembly histories, satellite distributions, star formation rates, and pair fractions. Working alongside new extra-galactic surveys, such as EUCLID, steel has the potential to be a prominent feature in the future of extra-galactic astrophysics.