In our pursuit of ever smaller transistors, with greater computational throughput, many questions arise about how material properties change with size, and how these properties may be modelled more accurately. Metallic nanocontacts, especially those for which magnetic properties are important, are of great interest due to their potential spintronic applications. Yet, serious challenges remain from the standpoint of theoretical and computational modelling, particularly with respect to the coupling of the spin and lattice degrees of freedom in ferromagnetic nanocontacts in emerging spintronic technologies. In this thesis, an extended method is developed, and applied for the first time, to model the interplay between magnetism and atomic structure in transition metal nanocontacts. The dynamic evolution of the model contacts emulates the experimental approaches used in scanning tunnelling microscopy and mechanically controllable break junctions, and is realised in this work by classical molecular dynamics and, for the first time, spin-lattice dynamics. The electronic structure of the model contacts is calculated via plane-wave and local-atomic orbital density functional theory, at the scalar- and vector-relativistic level of sophistication. The effects of scalar-relativistic and/or spin-orbit coupling on a number of emergent properties exhibited by transition metal nanocontacts, in experimental measurements of conductance, are elucidated by non-equilibrium Green’s Function quantum transport calculations. The impact of relativistic effects during contact formation in non-magnetic gold is quantified, and it is found that scalar-relativistic effects enhance the force of attraction between gold atoms much more than between between atoms which do not have significant relativistic effects, such as silver atoms. The role of non-collinear magnetism in the electronic transport of iron and nickel nanocontacts is clarified, and it is found that the most-likely conductance values reported for these metals, at first- and lastcontact, are determined by geometrical factors, such as the degree of covalent bonding in iron, and the preference of a certain crystallographic orientation in nickel. / Physics / Ph. D. (Physics)