Real-world structures operate under varying environmental and operational conditions, causing their dynamic properties to evolve over time. This non-stationary behaviour—observable across time scales from instantaneous to life-long—poses a major challenge for Structural Health Monitoring (SHM): how can we model and manage these changes to ensure reliable damage detection and remaining useful life assessment? In this keynote, we examine the primary sources of non-stationarity in structural dynamics and how they manifest in vibration data. We then introduce a parametric Bayesian time-series modelling framework that provides compact, accurate, and uncertainty-aware representations of non-stationary dynamics. This approach enables computationally efficient analysis while enhancing robustness for SHM, operational vibration monitoring, and digital twin applications. We show how these methods support simulation, prediction, and the development of damage diagnosis algorithms. Finally, we outline future perspectives, open questions, and opportunities that will shape next-generation modelling and SHM strategies.