Severe storms produce ocean waves with periods of 18-26 s, corresponding to wavelengths 500-1,055 m. These waves radiate globally as swell, generating microseisms and affecting coastal areas. Despite their significance, long waves often elude detection by existing remote sensing systems when their height is below 0.2 m. The new Surface Water Ocean Topography (SWOT) satellite offers a breakthrough by resolving these waves in global sea level measurements. Here we show that SWOT can detect 25-s waves with heights as low as 3 cm, and resolves period and direction better than in situ buoys. SWOT provides detailed maps of wave height, wavelength, and direction across ocean basins. These measurements unveil intricate spatial patterns, shedding light on wave generation in storms, currents that influence propagation, and refraction, diffraction and reflection in shallow regions. Notably, the magnitude of reflections exceeds previous expectations, illustrating SWOT's transformative impact.