Apologies if this is a little too modern for /r/AskHistorians, we can stop the discussion at 1996 if necessary. I tried looking for similar threads here and could not find any.
The root of my question is this: I've noticed in a lot of shows and movies (Mad Men for example) that passenger airliners of the 1960s are very similar to today's modern iterations. The major difference to my radically untrained eye is merely that modern airliners are less comfortable and more cramped due to cramming more people on board. Even the flight transit times seem similar. In other words, it seems like major innovation on passenger jets stalled between the 60s and today. Contrast this to the absolutely stunning rapid improvement of aviation between 1903 and WWII and it's a bit of a discrepancy.
Feel free to destroy any assumptions I have made!
(note: I am only interested in commercial transport aviation - obviously there have been rapid improvements to military aviation).
Airframes are somewhat lighter, leading to fuel savings.
Engines are much quieter and more fuel efficient and the development of engines and fuel systems enabling ETOPS (extended twin engine operations) have reduced maintenance costs materially.
Better flight control and avionics have enabled flight deck crews to drop from 3 to 2.
Effective aircraft ranges are far longer for every capacity class -- compare the range of a 777-300 to that of a 747-100 or that of the 737-700 to a DC-9, and regional jets to 1960s turboprops.
Airline and aircraft financing have gotten much more sophisticated and the industry has been deregulated for the most part.
So, all of this has meant more cheaper flights to more places at more times which are notably faster in the case of very long range non-stops and commuter hops now serviceable by regional jets.
The big improvements up to the 1960's were flying higher, faster and with more passengers. Flying higher meant flying above the weather. Eg. Rain, ice, turbulence, etc. Once planes could do that, there wasn't a need to fly any higher.
Planes flew faster and faster until they hit the sound barrier. Going faster than sound (Supersonic) has a number of inherent problems for both the aircraft and for people and buildings on the ground. During the 1960's there were studies to test supersonic passenger air travel over populated areas. The result was that supersonic flights were damaging to buildings and annoying to people. That is why the Concord only flew supersonic over the Atlantic. Close to the sound barrier was good enough. (Fun fact: modern passenger aircraft have a Mach meter to show speed related to speed of sound.)
The number of passengers on a single aircraft has been going up over time. Eg. 767, 777, A380. The limit there is that there a limited number of routes that need that many seats on one plane. Plus the airports must be able to accommodate that many people. If you have a 300 seat airplane you need an airport gate, security, etc that can handle 300 people. Then there is the time it takes to load 300 passengers. At some point it makes sense to have two flights of 150 passengers rather than one flight of 300.
The improvements you see now are related to making aircraft that are safer and more economical to operate. Fly by wire, fuel efficient bypass turbine engines, new wing designs, winglets, etc.