Structural Health Monitoring (SHM) assesses the integrity and safety of structures through in-situ sensor measurements. Despite its potential benefits, widespread adoption is hindered by the high sensor density required and the associated costs of data acquisition and processing. This talk introduces the concept of signature-informed modelling. The core idea is to develop a reduced-order model that captures just enough spatial and temporal information to estimate parameters of interest. In some sense, this approach focuses on the quality of the basis functions (for reliable parameter estimation) rather than their quantity (for accurate data reconstruction). To demonstrate its effectiveness, we present experiments on the challenging SHM problem of identifying impact events on structures using passive vibration measurements. Remarkably, the results show that accurate localization on planar structures can be achieved with a single strategically positioned accelerometer, whereas conventional wave-based methods typically require at least four sensors. Finally, we will discuss the integration of signature-informed principles into a hybrid modelling framework, which combines physics and data, to address real-world SHM scenarios.