Intense star formation and rapid black hole accretion in the centers of galaxies produce energy that propels gas outward. These galactic winds affect the evolution of their host galaxies, self-regulate the future growth of stars and black holes, and populate the enormous reservoirs of gas surrounding them. In the past decade, optical and near-IR integral field spectroscopy (IFS) from the ground has revolutionized the study of galaxy-scale outflows that reach into the their surroundings. The unprecedented infrared sensitivity, spatial resolution, and spectral coverage of the JWST IFUs is also transformative for studying these outflows at new, mid-infrared wavelengths. I will discuss observations of galactic winds driven by star formation and black holes at redshifts z ~ 0.5 that probe their extent and properties and illuminate the connection between galaxies and their surroundings.