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The air is less dense at higher altitudes, which means that aircraft need to be designed differently if they want to operate at higher altitudes. Some aircraft are designed for increased perfomance at these altitudes, and can fly faster, with better maneuvrability. 

To keep producing the necessary lift in the thinner air of high altitudes, planes need more thrust, which is why you'll likely see high performance, supersonic jets flying at those heights. These tend to have a sharper, needle-like nose, and sleeker, swept back wings, which helps the jet perform better at supersonic speeds. The SR-71 Blackbird is a high performance jet built to fly at over 24,000 m (80,000 ft).