Electrochemical impedance spectroscopy (EIS) is a powerful technique for noninvasively probing the internal state of many electrochemical systems. Unlocking the full capabilities of EIS requires the extraction of physically meaningful parameters from experimental spectra. Typically, this quantitative analysis is done by fitting equivalent circuit models (ECM). However, despite the widespread use of ECMs in the quantitative analysis of EIS spectra, huge opportunities exist for improving the physical interpretability, robustness, and reproducibility in the EIS analysis workflow. Combining physics-based models and experimental data, we explore the assumptions that determine equivalent circuit applicability and tradeoffs in circuit complexity vs. interpretability. We discuss approaches to improve the accuracy of impedance analysis including physics-based impedance models for lithium-ion batteries, confidence intervals and interactive visualization for ECM analysis, and encouraging best-practices through community-driven software. A web-based tool for analyzing experimental EIS spectra as well as a Python package for model fitting will also be presented.