Two years ago the Environmental Protection Agency reported aviation accounted for about three percent of the nation's CO2 emissions, or about twelve percent of transportation. The international figure is about two point five percent. These may not seem huge, but they've been growing steadily and, post pandemic, should continue their growth. Making matters worse is the global warming contribution from the cloud-like contrails produced by the jet engines at altitude. It's difficult to study, but indications are the contribution may double the global warming impact.
A number of approaches have been suggested and are in various stages of testing. Moving to bio-fuels isn't the greatest solution as growing and producing biofuels has issues and you're still producing contrails. In the short term some airlines will move to it, but that may be part a PR and carbon credits game as much as anything.
Electric airplanes exist and there are even a few (very) sort haul commercial flights. The problem is the specific energy of the battery - how heavy is a battery per unit of energy storage. Turbine fuel stores about eighty times as much energy as a safe lithium-ion battery of the same weight. Airplanes frequently carry large amounts of fuel - the weight of fuel burned on a cross country trip is greater than that of the the passengers and crew. The range of a battery powered airplane is severely limited even after accounting for the great efficiency of an electric motor. We could get a lot closer with exotic batteries that aren't anywhere close to reality, but even then you're talking about a propeller driven (slower) aircraft.
Hydrogen often comes up as the perfect clean fuel - the combustion product is just water. Although it's the most common element in the universe and accounts for most of your body's atoms, we need hydrogen gas and that's extremely rare on Earth. Hydrogen gas (H2) must to be produced and it takes a lot of energy to create it - more than you can get out of it. Most of it is produced from a petrochemical process that involves carbon emissions. This is called black or grey hydrogen and, if you manage to capture most of the carbon emissions it's called blue hydrogen. What you want is green hydrogen - hydrogen produced using electrolysis with electricity from wind, solar or nuclear power. That seems like a nice use of excess intermittent power.
It's important to think of hydrogen as an energy storage medium - a non-rechargeable battery of sorts. It has a very low - essentially unusable energy density at atmospheric pressure. You'd need impossibly large tanks (think about Hindenburg sized tanks) or you can compress it or liquify it and shrink your tanks to something more manageable. In gas form at a very high but probably safe pressure it needs about five to ten times the volume of jet fuel. Liquid hydrogen gets you down to about three and a half times the volume.
Engineering is all about finding an optimal solution to several problems that generally interact. You could convert a turboprop or turbofan to burn hydrogen and see where that takes you. Turboprops seem to be workable on short haul routes (1,000 km or less) with small passenger loads (under 100 passengers). They'd be slow and fly at lower altitudes than today's jets. Turbofans present a number of problems - at altitude they're making contrails and the range and payload isn't great. One needs to think a bit out of the box.
You might use a hybrid jet fuel/hydrogen engine that climbs to cruising altitude on jet fuel as fuel consumption is much greater in that phase. Then the switch to hydrogen fuel is made when the engines are throttled back at cruise altitude. You could also design a lifting body aircraft that has a lot of internal volume for liquid hydrogen fuel tanks without being too large for conventional airports. Tricks might get you across the US with a few hundred passengers, but flights across the Atlantic or Pacific would require something more.
The prop-driven airplanes present other opportunities. A fuel cell converts hydrogen to electricity and electric motors are more efficient that jet engines. There are a number of little problems that can be overcome, but a fuel cell propeller airliner may just be a short to medium range solution.
I didn't go into the NOx problem. The high heat of combustion in a jet engine creates nitrous oxides when the nitrogen in the air is heated to high temperatures. That's a problem - particularly at the high altitudes jets fly at and burning hydrogen won't fix it. The way around it is to use fuel cells and electric motors, but that's for lower altitudes and slower speeds. There isn't an ideal solution - you just hope to reduce as much as you can.
Airbus is working on the problem - or at least they were before the pandemic. I can believe the target date for the propeller aircraft, the lifting body is probably more than fifteen years out.
There may be a near term niche for hydrogen powered flying vehicles. Agricultural and inspection drones are much larger than hobbyist drones. They're limited to half hour flight times with batteries, but new fuel cell drones with small high pressure hydrogen tanks have appeared in Korea. They can fly for hours and that may be the first practical opening for aerial hydrogen.