Abstract Atmospheric retrievals of exoplanetary transmission spectra provide important constraints on various properties, such as chemical abundances, cloud/haze properties, and characteristic temperatures, at the day–night atmospheric terminator. To date, most spectra have been observed for giant exoplanets due to which retrievals typically assume hydrogen-rich atmospheres. However, recent observations of mini Neptunes/super-Earths, and the promise of upcoming facilities including the James Webb Space Telescope (JWST), call for a new generation of retrievals that can address a wide range of atmospheric compositions and related complexities. Here we report Aurora, a next-generation atmospheric retrieval framework that builds upon state-of-the-art architectures and incorporates the following key advancements: (a) a generalized compositional retrieval allowing for H-rich and H-poor atmospheres, (b) a generalized prescription for inhomogeneous clouds/hazes, (c) multiple Bayesian inference algorithms for high-dimensional retrievals, (d) modular considerations for refraction, forward scattering, and Mie scattering, and (e) noise modeling functionalities. We demonstrate Aurora on current and/or synthetic observations of the hot Jupiter HD 209458 b, mini Neptune K2-18b, and rocky exoplanet TRAPPIST-1 d. Using current HD 209458 b spectra, we demonstrate the robustness of our framework and cloud/haze prescription against assumptions of H-rich/H-poor atmospheres, improving on previous treatments. Using real and synthetic spectra of K2-18b, we demonstrate an agnostic approach to confidently constrain its bulk atmospheric composition and obtain precise abundance estimates. For TRAPPIST-1 d, 10 JWST-NIRSpec transits can enable identification of the main atmospheric component for cloud-free, CO2-rich, and N2-rich atmospheres and abundance constraints on trace gases, including initial indications of O3 if present at enhanced levels (∼10×–100× Earth levels).