Staring from the ground there are three layers of the atmosphere: troposphere (temperature falls with altitude), stratosphere (temperature increases with altitude) and the mesosphere. The radius of the stratosphere is 11 km (at the poles) and 17 km (at the equator). The stratosphere is in radiative equlibrium and thus stratified (stable against convection; whence the name). The stratosphere is virtually dry.
Jets fly in the lower stratosphere (9-12 km) because one obtains higher fuel efficiency when the ambient medium is cool.
The Stratospheric Observatory for Infrared Observatory (SOFIA) is the primary competition. SOFIA is a 2.5-m telescope hosed in a modified Boeing 747-100 (Boeing 747SP; designed for ultra long hauls). The flying altitude of SOFIA i 41,000 (12 km).
Unmanned areal vehicles (UAVs; sometimes mis-named as Unmanned Air Vehicles) constitute the fastest growth in defence. Lacking a pilot the costs of using these vehicles either for reconnaissance or for missile launches (drones). The use of an U2 for CMB studies (Smoot, Gorenstein and Muller 1977, PRL) was perhaps the first astronomical use of high altitude airplanes. (Surprisingly) The primary scientific use of UAVs has been to send spacecraft into inclement weather (e.g. aeronomy studies) or dangerous areas (e.g. studying great fires).
The unmanned spy plane, RQ4 Global Hawk, has an endurance of 36 hours and a service ceiling of 20 km (65,000 feet). Typically it is used for SAR mapping or long-wavelenght imagery of a combat theater. Can take a ton or two of payload. Not cheap ($50M).