What-if: Jet Engine Technology doesn't Exist

There is already a “What-if” topic about aircraft, but this is a little different:

Imagine, if you will, that the turbojet was never invented or discovered. For whatever reason, the jet engine of all kinds is never invented/brought into service since it is too expensive/not viable/never discovered/whathaveyou. Frank Whittle decided to invent the a new flavor of Ice Cream instead of the jet engine.

How would have military aircraft developed if they never used jet engines? We would have continued through the cold war to today using prop engines or some other form of propulsion; anything other than jet power. However, rocket technology is available, so we could have missiles and rocket-propelled aircraft and what-have-you.

I know that there were those which were working on some very advanced prop designs (supersonic propeller, dual-prop, pusher-puller, and the flying pancake). What kind of technologies would have arisen for aircraft propulsion in the absence of jet power? Rocket technology? Would we forever remain subsonic except for specialized rocket-propelled aircraft?

I know it’s a little hard to press that jet technology would NEVER go discovered; after all, it would probably rise out of rocket technology at SOME point. But just presume that Jet Technology never exists whatsoever, for whatever reason.

How would aircraft look today without Jet Technology?