The manipulation of magnetic textures at the nanoscale presents new horizons for computing technology. As conventional electronic devices reach their physical limits, magnetic skyrmions — topologically non-trivial whirls of a material's magnetisation — offer a promising solution for next-generation information processing, requiring minimal energy and electric current for manipulation.

In this thesis, we investigate the application of magnetic skyrmions in both fundamental spintronic transport and reservoir computing. Our work advances two key areas: first, a theoretical understanding of the skyrmion Hall effect in topologically neutral structures, and second, the development of skyrmion-based reservoir computing. Beginning with a foundational analysis of topological effects in magnetic systems, we contribute to the understanding of skyrmion dynamics under spin torques and then proceed to demonstrate the potential of skyrmions for computation through reservoir computing.

Our investigation is structured in two major sections. The first part provides a comprehensive theoretical treatment of current-driven skyrmion dynamics. We develop our theoretical framework through micromagnetic modelling. Our findings challenge the notion that topologically neutral magnetic structures, such as antiferromagnetic skyrmions and skyrmioniums with net-zero winding number, can eliminate the skyrmion Hall effect through balancing Magnus forces. Furthermore, we demonstrate that this assumption fails when these structures are driven by spin-orbit torques. Our analysis employs the collective coordinate dynamics approach and is validated through extensive numerical simulations.

The second part explores novel applications of skyrmions in reservoir computing, where we create a skyrmion fabric reservoir that exploits the collective dynamics of skyrmions for computation. Focusing on nonlinearity and memory — the fundamental requirements for reservoir computing — we develop novel task-agnostic spatial metrics that enable localised measurement of these crucial properties. Unlike conventional reservoir metrics, our approach allows parallel evaluation from a single input signal, enabling efficient parameter optimisation. We demonstrate the inherent trade-off between memory capacity and nonlinearity in our reservoir's behaviour, both locally and globally, and show how balancing these properties enhances task-specific performance. These metrics allow optimisation of readout node placement and reveal the spatial distribution of computational properties in magnetic textures. Using these insights, we develop an optimised skyrmion reservoir by tuning key material parameters, including Dzyaloshinskii-Moriya interaction strength and anisotropy. We then show how this in materia computing approach enables direct spatio-temporal pattern recognition in physical matter without requiring millions of interconnected artificial neurons. The multi-channel skyrmion reservoir we develop for this purpose achieves the highest performance yet reported for in materia reservoir computers in spoken digit classification, whilst maintaining the inherent advantage of magnetic skyrmions such as energy efficiency.