Whilst Southflite's answer is both comprehensive and my records show it is pretty accurate, the original question is invalid as it is incomplete.
When will enthusiasts learn that you cannot "age" an aircraft by using the term "oldest". In aviation it is meaningless.
Airframes (not aircraft because engines and other parts get changed) have a number of clocks running.
The first, only because it applies to pressurised and unpressurised aircraft, is spar life ( and some aircraft can be re-sparred cost effectively).
The next clock, exposure, applies to all airframes and various anti corrosion treatments and replacement parts can keep that one ticking for years.
The first two clocks can, therefore be "rewound" and this explains how the DC3 and other unpressurised aircraft keep flying in numbers and why some of the big prop water bombers, which are never now pressurised, keep flying.
The remaining clocks apply to all pressurised aircraft. Each airframe has a "life" determined by the manufacturer and, in many cases, this gets extended as the type ages and various extensions are worked in.
The life is finite, however, and is measured by three clocks:
Rotations, i.e how many times an aircraft has been pressurised/depressurised
Actual calendar age.
The last is the least significant and only comes into play for marketing purposes when it gets around that XXX airlines is flying 25 year old aircraft and the "Gee Wilma, you ain't flying with them, I change may car every two years" syndrome sets in.
Short haul aircraft do more rotations than long haul aircraft and tend to do less hours than long haul aircraft which have less rotations for more hours.
So, a B737 and a B747 both built in 1970 and both having "normal" major airline careers would end with vastly different hours and rotations at the time of scrapping.
747s have been getting over 100,000 hours but only 23,000 or so rotations. The 737s have been doing around 60,000 hours and up to 40,000 rotations.
Given the intensity of 737 operation against that of the 747, it is likely that the 737 would be scrapped before the 747.
A 747 can easily be 30 years old and, if properly maintained and used on long haul exclusively, have a very high number of hours yet be "young" in terms of rotations.
The same applieds to Concorde. If they ever fly again, the BA aircraft, though 25 years old, are only at mid life, the under used Air France machines are "younger".
All Concordes are used on a phased basis and the high time aircraft has only 24,000 or so hours out of the currently projected 40,000 hours.