Most modern jet powered aircraft spend a considerable amount of time in the transonic state. This is particularly important due to an effect known as wave drag, which is prevalent in these speed ranges. Attempts to combat wave drag can be seen on all high-speed aircraft; most notable is the use of swept wings, but another common form is a wasp-waist fuselage as a side effect of the Whitcomb area rule.
Severe instability can occur at transonic speeds. Shock waves move through the air at the speed of sound. When an object such as an aircraft also moves at the speed of sound, these shock waves build up in front of it to form a single, very large shock wave. During transonic flight, the plane must pass through this large shock wave, as well as contending with the instability caused by air moving faster than sound over parts of the wing and slower in other parts. The difference in speed is due to Bernoulli's principle.
Transonic speeds can also occur at the tips of rotor blades of helicopters and aircraft. However, as this puts severe, unequal stresses on the rotor blade, it is avoided and may lead to dangerous accidents if it occurs. It is one of the limiting factors to the size of rotors, and also to the forward speeds of helicopters (as this speed is added to the forward-sweeping (leading) side of the rotor, thus possibly causing localized transonics).
In Astrophysics where ever there are evidences of shocks (standing, propagating or oscillating) the flow close by must be transonic as only supersonic flows form shocks. Interestingly all the black hole accretions are transonic (S.K. Chakrabarti, ApJ, 1996, v. 471, p. 237), many of the flows also have shocks very close to the black holes.
The outflows or jets from young stellar objects or disks around black holes can also be transonic since they start subsonically and at a far distance they are invariably supersonic. Supernovae explosion is accompanied by super sonic flows and shock waves. Bow shocks formed in solar winds around the earth is a direct result of transonic wind from the sun.