Aerobatics

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In the early days of flying, pilots realised that their aircraft could be used as part of a flying circus to entertain people or impress others by performing aerobatics. Maneuvers that had no practical purpose were flown for artistic reasons or to draw gasps from onlookers. In due course some of these maneuvers were found to allow aircraft to gain tactical advantage during aerial combat or "dog fights" between fighter aircraft. The word presumably derives from the term used by human gymnasts - acrobatics - to describe exercises designed to impress or build muscle strength.
Many aerobatic maneuvers involve rotation of the aircraft about its longtitudinal axis - rolling - or the pitch axis - looping. Some complex maneuvers - such as a spin (flight) - also require that the aircraft be displaced around a vertical axis, known as yawing. Maneuvers are often combined which demands a higher level of skill from the pilot, but greatly increases the spectacle of an aerobatic flight sequence.
Formation aerobatics are usually flown by teams of up to sixteen aircraft, although economic considerations mean that most teams habitually fly between four and ten aircraft. Some are state funded to reflect pride in the armed forces whilst others are commercially sponsored. Coloured smoke trails may be emitted to emphasise the patterns flown and/or the colours of a national flag. Usually each team will use aircraft similar to one another finished in a special and dramatic colour scheme, thus emphasising their entertainment function.
Aerobatic aircraft usually fall into two categories - specialist aerobatic, and aerobatic capable. Specialist designs such as the Pitts Special, the Diabolo, the Extra 200 and 300, and the Sukhoi Su-29 aim for ultimate aerobatic performance. This comes at the expense of general purpose use such as touring, or ease of non aerobatic handling such as landing. At a more basic level, aerobatic capable aircraft can be dual purpose - equipped to carrying passengers and luggage, easy to land, as well as being capable of basic aerobatic figures.

Aerobatics Model Aircraft
and 3D-capable model airplanes are aircraft with large control surfaces. They are very agile. 3D-model aircraft have thrust that is greater than the weight. This enables the model to climb vertically at constant or increasing speeds, hence "3D". It also allows the model to fly with the wing partially or full stalled, hovering on the prop thrust.