While several breakthroughs were made in recent years, the full potential of electrochemical impedance spectroscopy (EIS) for the analysis of (bio)electrochemical systems has yet to be fully explored. In this interdisciplinary research project, expert collaborators and I seek to advance the impedimetric analysis and characterization of electrochemical power sources, bacterial biofilms, and plants through novel measurement and mathematical modeling approaches. The state variables of Lithium-ion batteries and fuel cells will be determined using probabilistic modeling approaches, and a novel compressed sensing-based approach for deconvoluting the distribution of relaxation times (DRT) will be developed. An in-depth and explainable impedimetric characterization of biological systems will be achieved through the transfer of modeling progress from electrochemical power source analysis. Interpretable DRT profiles will be unraveled for bacterial biofilms through an extensive analysis of mutant libraries. Furthermore, we will explore the use of microelectrode arrays for a performant multi-label classification and composition analysis of multi-species biofilms. Plant stress physiology and fruit ripening are two applications of plant biology for which we propose non-invasive impedimetric measurement and modeling approaches. Finally, we will develop open-source software and establish a public data repository for EIS measurements to accelerate overall progress in the field.