Hyperdimensional (HD) computing is a novel approach to machine learning inspired by neuroscience, which uses vectors in a hyper-dimensional space to represent data and models. This approach has gained significant interest in recent years with applications in various domains, one of which being biomedical applications. However, wearable biomedical applications pose a broad range of challenges for hyperdimensional computing that must be tackled before its potentially widespread adoption. I focus on epilepsy detection as a use case and use it for improving and testing the proposed HD computing methods, as it is a chronic neurological disorder that affects a significant portion (0.6 to 0.8%) of the human population and imposes severe risks in the daily life of patients. Despite advances in machine learning and Internet of Things (IoT), small and non-stigmatizing wearable devices for continuous monitoring and detection in outpatient environments are not yet widely available. Thus, the main motivation of my thesis was twofold; first, to explore the advantages and limitations of hyperdimensional computing for biosignal monitoring, and second, to develop new approaches for epilepsy detection. I demonstrate and develop additional aspects in which HD computing, and the way its models are built and stored, can be used to understand further, compare, and create more complex machine-learning models for epilepsy detection. These possibilities are not feasible with other state-of-the-art models, such as random forests or neural networks. More specifically, I propose new ways to improve two main parts of the HD computing workflow: encoding and learning. Different methods to encode three-dimensional sets of information (features with spatial and temporal information) are proposed and discussed. Next, due to the highly personalized nature of epileptic seizures and their unbalanced nature, learning is improved by proposing a new multi-centroid learning approach. Then I study the interplay between personalized and generalized models. The process of creation of generalized models from personalized ones is studied, which is interesting for future distributed learning applications. Next, I show that HD computing enables combining personalized and generalized models forming hybrid models, resulting in increasingly performant epilepsy detection. Finally, such models are used to test the knowledge transfer between different datasets, making a first step towards the integration of knowledge from available epilepsy datasets. The need for interpretable models and predictions in healthcare applications is paramount, and this PhD thesis demonstrates the possibility of HD computing for visualizing prediction decisions in time, per features, and also per channels. Also, the process of feature and channel selection using HD computing encoding is explored. In the end, I led the development of HDTorch, an open-source PyTorch-based library that enables much faster exploration and development of HD computing algorithms. Overall, I demonstrate how HD computing can help bring wearable and interpretable healthcare systems closer to reality and patients' everyday life. Despite using epilepsy as a representative use case, all the work proposed is easily translatable to other biomedical signals and applications. Thus, I believe it can inspire and foster further improvements in the hyperdimensional computing field and in wearable healthcare applications.