The chemistry of galaxies provides a powerful probe of the underlying physics driving their evolution, complementing the traditional tools of morphology, kinematics,and colours. This dissertation examines several aspects of the galactic chemical evolution of late-type galaxies - both disc-like and dwarf - using a suite of cosmological hydrodynamical simulations, which incorporate the nucleosynthetic pollution of the interstellar medium, supplemented with classical analytical models of Local Group dwarfs. Throughout the work, these models are confronted with extant observations of both local and high-redshift systems, in order to identify both the strengths and weaknesses of the current generation of galaxy models. The work here has been presented across four primary science chapters which follow on from the Introduction and Motivation, prior to closing with the Conclusions and Future Directions. The first science result (Chapter 2) derives from an examination of the cold (neutral)gas content of the first-ever simulated bulgeless dwarf disc galaxies (Governato et al. 2010), and builds upon the work first presented in Pilkington et al. (2011). The focus of the work is on comparing the observables inferred from the simulated interstellar media, with those seen in nature (including The HI Nearby Galaxies Survey and the Magellanic Clouds), including their velocity dispersion profiles, disc flaring, and the distribution of power within the ISM’s structure, on different scales. Going beyond the work in Pilkington et al. (2011), two additional simulations from the Governato et al. (2010) suite are included, and the original work has been extended to include an analysis of the chemical properties of the dwarf galaxies. The second science result (Chapter 3) examines the role of feedback, metal diffusion, and initial mass function selection, on the resulting chemistry of a new grid of M33-like disc simulations. The emphasis of the analysis is upon the resulting age-metallicity relations and metallicity distribution functions (in particular, the extreme metal-poor tail). Aspects of the work have been presented by Pilkington et al. (2012b), enhanced here by a further examination of the satellites associated with their respective host galaxies. The satellites are seen to be free of gas, with star formation histories which make them not unlike Local Group dwarf spheroidals. The third science result (Chapter 4) is based upon an analysis of the temporal evolution of metallicity gradients in Milky Way-like systems, and derives from the work presented in Pilkington et al. (2012d). A large suite of simulations, sampling a range of numerical codes (particle- and grid-based, in addition to classical Galactic Chemical Evolution (GCE) models), each with different treatments of star formation, energy feedback, and assembly histories, was employed. The analysis focussed on both the radial and vertical abundance gradients, emphasising the role of feedback in shaping the gradients, and demonstrates the critical role that new observations of in situ gradients at high-redshift can play in constraining the uncertain nature of feedback within simulations. This work has been complemented by a brief examination of the azimuthal abundance variations in the massive discs. The fourth science result (Chapter 5) expands upon our earlier exploration of the chemical properties of simulated dwarf galaxies, but now employs a classical semi-numerical GCE approach. By coupling colour-magnitude diagram-constrained star formation histories with our GEtool GCE code, we attempt to constrain the relative rates of gas infall and outflow, for the Carina, Fornax, and Sculptor Local Group dwarfs, in order to match their empirical chemical abundance patterns and metallicity distribution functions. This builds upon the preliminary work, as presented by Pilkington & Gibson (2012a).