There are many computer vision applications including object segmentation, classification, object detection, and reconstruction for which Machine Learning (ML) shows state-of-the-art performance. Nowadays, we can build ML tools for such applications with real-world accuracy. However, each tool works well within the domain in which it has been trained and developed. Often, when we train a model on a dataset in one specific domain and test on another unseen domain known as an Out-of-Distribution (OOD) dataset, models or ML tools show a decrease in performance. Previously, in the literature different solutions have been proposed to tackle with Domain Shifting problem which occurs during the inference of models, like adversarial training, feature alignment, learning distribution invariant features, meta learn- ing and many more. Similarly, to understand the behaviour of ML models for serious challenges of Domain Generalisation (DG), Domain Adaptation (DA), and Domain Shifting, in summary, this thesis presents novel work at the intersection of vision-based technologies for domain-specific and domain-generalised methods, vision transformers for DG, synthetic data generation for OOD data with detailed analysis, and the effects of pruning on DG. The underlying hypothesis is that to solve complex challenges like DG and DA, “it is possible to say that domain-generalised learning which can refer to dynamic learning could be better than domain-specific learning which can refer to static learning”. It means that under domain shifting, dynamic learning can also have better, reliable, and faster adaptation than static learning. Some initial experiments are conducted on two popular vision-based benchmarks, PACS and Office Home and we introduce an implementation pipeline for domain generalisation methods and conventional deep learning models. The results illustrates that domain generalised models have better accuracy than domain specific methods for these chosen benchmarks. Since domain generalisation involves pooling knowledge from source domain(s) into a single model that can generalise to unseen target domain(s), recent trends motivate us to conduct an investigation into the factors which could affect the DG ability of a model and this inspired us to explore vision transformers. Initially, we examined four vision transformer architectures namely ViT, LeViT, DeiT, and BEIT on out-of-distribution data. Due to advantages like self-attention, self-supervised fine-tuning, and mask image modeling, we use the BEIT architecture for further experiments on three benchmarks PACS, Home Office, and DomainNet. In summary, under few conditions and selected measurement metrics, our experiments demonstrate that it is true to say domain generalised learning provides better solutions than domain specific learning.