"Near-space" is officially the region that lies between 75,000 feet (23km) and and 62.5 miles (100km) above the Earth's surface according to the International Aeronautical Federation (FAI). Weather balloons routinely ascend to 90,000 feet (27km) and scientific balloons ascend even further, to 135,000 (over 40 km) where they may remain for several days.
The image above (by kind permission of Robert Harrison) was taken from his Icarus 1 balloon, which achieved an altitude of 35,015 meters (35 km or almost 22 miles) and demonstrates the astonishing "aerial" photography results that can be obtained with comparatively cheap and simple equipment.