Biomedical signal processing, with its transformative nature, has emerged as a multidisciplinary field in recent times. By bridging engineering, computational neuroscience and clinical medicine, this field provides a powerful tool for improving healthcare outcomes. With rapid advances in sensing technologies, imaging modalities such as EEG, MEG, MRI, fMRI not only allows us to capture the brain’s intrinsic activity with detail but also offer opportunities for early detection and prediction of neurological conditions. Neuroscience comes with its own challenges, and one such central challenge is understanding how behavior and cognition emerge from complex brain networks. This understanding has direct links to various medical and psychological conditions such as epilepsy, Alzheimer's, schizophrenia, stroke, among others. Disrupted neural activity is often associated with such conditions and traditional signal processing along with machine learning approaches do offer important insight into them. However, the nonstationary and dynamic nature of neural signals demand more advanced technologies. Graph Signal Processing (GSP) provides one such advancement. Different brain regions specialise in distinct functions and their local-global communication is critical for healthy cognition. GSP is promising as it provides a natural framework to capture both local and global level dynamics and connectivity patterns in neural activity. Such approaches can help clinicians distinguish disrupted neural activity, identify reliable biomarkers of disease and improve health care. The primary objective of our work is to advance real time biomedical signal processing for the purpose of early detection, accurate prediction and monitoring of neurological disorders affecting millions of people worldwide. By developing tools that are clinically relevant, we aim to support healthcare systems in making early and more accurate diagnosis, tracking disease progression and developing personalised interventions. At the same time, these methodologies developed for healthcare, can also extend to settings beyond healthcare. Various applications such as cognitive workload assessment, adaptive human-machine interaction, neuromarketing and even truth lie detection are built on similar core principles. These areas, though secondary to our main area of interest in healthcare, exemplify the broader societal impact of innovations in biomedical signal processing.