This project aimed to develop improved spectral synthesis models for core-collapse supernovae. Supernovae play an important role in modern astrophysics, as the end-points of massive star evolution, the production sites of most elements between oxygen and nickel in the periodic table, and the birth places for neutron stars and black holes. A better understanding of these events, in and in particular their explosion physics and element production, requires advanced spectral modelling tools and analysis. Development of techniques can also find use in other science areas such as atmospheric climate modelling, with broad benefits for society. The project contained three main objectives: 1) To develop the first spectral predictions for 1D neutrino-powered supernovae, 3) To develop 3D code capability, and 3) To use this 3D code to analyze current 3D hydrodynamic models. The first project highlights that not only dimensionality is important in modelling, but also realistic stellar evolution and explosion physics. We produced in this work package the first spectral predictions of neutrino-powered models, and by comparison with observations could draw a strong conclusion that the class of low-velocity Type II supernovae likely originate from low-mass progenitors, 8-10 solar masses. A 3D code version has been successfully developed, although with some more limited microphysical treatments compared to the 1D version. This 3D code is nevertheless a major breakthrough, and the code is currently being used to analyze spectral predictions from 3D explosion models. We expect this to give a series of papers with significant new results with regard to how element production can be inferred from observed lines, and how the supernova explosion occurs.