Why do jet engines smoke?
Smoke in jet engines is usually from unburnt or partially burnt fuel (or by water injection). Early jet engines used to create a lot of smoke due to these reasons (and due to lack of environmental regulations).

 

KC 135 engines creating smoke due to water injection By USAF Photographer - USAF photo, Public Domain, Link

Water injection, while cooling the engine, quenches the flames to an extent, resulting in unburnt fuel, which comes out as smoke. However, aircraft have moved away from water injection, reducing emissions.

Another reason for the smoke is inefficient combustion- older jet engines (turbojets in first aircraft and low bypass turbofans) were not as efficient as engines today, which premix the fuel with air and pre-vaporise it before combustion, rather than using droplet combustion- basically mixing fuel more evenly with air. Requirements of fuel efficiency along with stricter regulations mean that engines today have less emissions compared to their predecessors.



Smoke during Boeing 707 takeoff; image from nycaviation.com

In this case re-engining the aircraft with more efficient ones usually results in a reduction of smoke. For example, the USAF re-engined the KC-135s (from Pratt &amp; Whitney J-57-P-59W turbojet to the CFM International CFM56 turbofan), which along with the elimination of water injection, reduced smoke.




On the top is KC-135s from an exercise in 1979; image from network54.com. Below that is KC-135Rs from Singapore Airforce; image from reddit.com