Solidification is a phase transformation of utmost importance in material science, for it largely controls materials' microstructure on which a wide range of mechanical properties depends. Almost every human artifact undergoes a transformation that leads to a solid phase, be it via well-established manufacturing processes as casting or forging, or more recent technological advances such as 3D printing. This thesis aims to study some fundamental aspects of solidification, focussing in particular on metals and alloys. Despite being a phenomenon investigated for a long time with both experiments and theoretical models, solidification still involves a very complex set of phenomena that requires a multi-scale approach to provide useful insights. For example, properties relating to the thermodynamics and kinetics of solid-liquid interfaces play a crucial role in micro-scale modeling of solidification, yet are particularly challenging to assess with experimental techniques. Our main instrument of investigation has been a set of well-established computer simulation techniques at the atomic scale, and we applied and extended some of these methods, with the primary goal of improving the reliability of some results related to the properties of solid-liquid interfaces and being able to study systems whose level of complexity comes closer to that of interest to some real manufacturing processes. The approach of atomistic simulations involves several technical and theoretical problems. A first issue is related to the size of the systems that it is necessary to simulate to obtain results of some relevance despite an inherent statistical error that is often substantial. Moreover, some theoretical subtleties, such as the arbitrariness in the definition of the interface, inevitably emerge from an approach at the atomic scale, and they lead to problems whose solution is anything but univocal; often, in fact, different formulations of these problems provide different results. The first contribution of this thesis focused on extending a computational method that serves to calculate a fundamental quantity known as interface free energy and, in particular, to decrease its computational cost by reducing the number of particles of the simulated systems. The second contribution addressed the study of crystal-melt interface properties of a particular metallic binary alloy. The idea behind this part of the work was to combine different techniques of atomistic simulations whose outcomes make it possible to obtain an exhaustive description of both the thermodynamics and the dynamics of the interfaces. We have based this approach on a precise definition of dividing surface, and we have derived all our results in a consistent way allowing us to eliminate some arbitrary choices that similar kinds of simulations usually entail. A part of the results obtained confirmed the reliability of our approach, showing satisfactory agreement with some other established results. However, challenges remain associated with the accuracy of the interatomic potential, the presence of significant finite-size effects, and the difficulty in converging to satisfactory statistical accuracy the thermodynamic and dynamical properties of solid-liquid interfaces.