Charged particle track finding and fitting is one of the most computationally complex and expensive parts of event reconstruction at High Energy Physics collider experiments, in particular for experiments such as ATLAS at the Large Hadron Collider, and its future High-Luminosity upgrade. As collision rates continue to rise in order to provide increasingly large data sets for analysis, the challenges associated with track reconstruction are exacerbated further due to the combinatorial nature of the track finding task and the high measurement density. As a result, track reconstruction is an area where new computational approaches to the various aspects of the problem can be extremely beneficial. Consequently, track reconstruction software should consider the implications of developments and trends in computing architectures. For example, the move towards wide registers in GPUs which benefit from increased parallelism, and the necessity to explore multi-threading to efficiently use limited available resources. Adapting experiments’ track reconstruction towards such paradigms is challenging for several reasons. The highly sequential nature of the track reconstruction chain means that intra-algorithm rather than inter-algorithm parallelism must be considered, and the probable non-homogeneity of available computing resources will mean that GPU-optimized code must either run efficiently also on CPUs, or be limited to specific use cases. Identifying such cases and performing the necessary code refactoring are highly relevant challenges.