Encircling our planet at distances of 2.5 to 8 Earth radii is a dynamic plasma population known as the ring current (RC). During geomagnetic storms, the solar wind's interaction with Earth's magnetic field pumps petaJoules of energy into the RC, energizing and transporting particles. To measure the global geospace response, RC imaging is performed by capturing energetic neutral atoms (ENAs) created by charge exchange between geospace ions and the neutral exosphere. The H exosphere is itself imaged via its geocoronal Lyman‐α glow. Two Wide‐angle Imaging Neutral‐atom Spectrometers (TWINS) is a stereoscopic ENA and Lyman‐α imaging mission that has recorded the deep minimum of solar cycle (SC) 23 and the moderate maximum of SC 24, observing geospace conditions ranging from utterly quiet to major storms. This review covers TWINS studies of the geospace response published during 2013 to 2017. Stereo ENA imaging has revealed new dimensionality and structure of RC ions. Continuous coverage by two imagers has allowed monitoring storms from start to finish. Deconvolution of the low‐altitude signal has extended ENA analysis and revealed causal connections between the trapped and precipitating ion populations. ENA‐based temperature and composition analyses have been refined, validated, and applied to an unprecedented sequence of solar activity changes in SC 23 and SC 24. Geocoronal imaging has revealed a surprising amount of time variability and structure in the neutral H exosphere, driven by both Sun and solar wind. Global models have been measurably improved. Routine availability of simultaneous in situ measurements has fostered huge leaps forward in the areas of ENA validation and cross‐scale studies. Plain Language Summary This paper is a review of the last several years of science results from the National Aeronautics and Space Administration (NASA) Two Wide‐angle Imaging Neutral‐atom Spectrometers (TWINS) mission, which performs imaging of the near‐Earth space environment, known as geospace. TWINS geospace imaging has revealed new structure and behavior in the ionized and neutral gases surrounding the Earth during geomagnetic storms—disturbances in the plasmas and fields caused by changes in the solar wind. Key Points Stereo ENA imaging has revealed new dimensionality and structure of ring current ions; LAE analysis has revealed causal connections Ion temperature, ion composition, and neutral exospheric H density have been imaged for events spanning solar cycles 23 and 24 Global models have been measurably improved, and multimission observations have enriched the study of the cross‐scale geospace response