Degradation of lithium battery cells is a complex process occurring over multiple temporal and spatial domains. Improved understanding of cell health is a prerequisite for expanded use of Li-ion battery technology in many challenging applications. Early detection of changes in critical parameters would enable performance assessment and degradation forecasting, as well as providing a route to predict the most likely eventual failure modes. Parameter detection requires the ability to measure a diverse set of static and dynamic properties that elucidate the state of a battery system. To enable efficient and safe battery operation, diagnostic schemes need to be fast, accurate, and reliable, work in near real-time, and detect potential faults as early as possible; to enable widespread practical adoption, parameter detection must be achieved with minimal added cost. In tandem, the need to run accurate in-service battery models is critical, and would enable model-based control. Second only to safety monitoring of voltage and temperature, state-of-charge (SOC) estimation is the most important function of a battery management system (BMS). Better BMS SOC could help maximize battery performance and lifetime, but is often accurate to only +/- 10% - and simple methods to improve this accuracy do not currently exist. Models capable of predicting Li-ion performance under modest conditions are highly advanced. But significant progress is still needed to couple operational models suitable for the diagnosis and prognosis of degradation and failure with models of degradation mechanisms. Generally faults and the resulting degradation manifest as capacity or power fade and often state-of-the-art techniques such as X-ray CT, open circuit voltage measurements, and thermal measurements are used to characterise the degradation. This proposal brings together a world-class team to address the critical issue of degradation and health estimation for leading lithium-ion-battery chemistries. We place particular focus on Translational Diagnostics, which we define as diagnostic methods that translate across length scales, across different domains, and across academic research into industry practice. Key outputs from our work will be a suite of new and validated diagnostic tools integrated with battery models for both leading and emerging lithium-ion and sodium- ion battery chemistries. We aim to ensure that these diagnostic tools are capable of cost-effective deployment on both small and large battery systems, and able to run in real time with sufficient accuracy and reliability, such that safer, more durable and lower cost electrochemical energy storage systems can be achieved