Aircraft

Overall
Aircraft launch from their base air/landship or building and autonomously attack their parent's target. In theory, Tri- and Bi-planes can engage other aircraft (all aircraft can engage airships), though it's unclear how they prioritize doing so. Crew piloting an Aircraft are not counted as present aboard their parent under the Crew indicator. If you're wondering why your undamaged aircraft carrier is missing crew, that's why.

Aircraft have unlimited fuel, and can continue after their parent module/ship has been knocked out. Should all ships/structures of their side be knocked out, however, they'll be lost as well.

Planes
All planes launch and land laterally, but require no runway. It's perfectly acceptable to chain planes end-to-end and they'll have no problems taking off or landing. If you're using a ship as the parent for planes that'll need to land during the battle (Torpedo Bombers, or planes damaged by anti-aircraft fire), planes frequently can't land on the ship while it's moving, so hold it steady if you see a plane on approach.

One advantage to using planes is that since they don't use Suspendium, they can engage targets at any altitude: for example, Bombers attacking a Moon Disk will successfully bomb it despite being so high the screen won't scroll up to show them.

Biplane
The Biplane hangar is a 6x1 module. It is external (no armor bonus) and blocks the top of it from further modules.

Triplane
The Triplane hangar is a 6x1 module. It is external (no armor bonus) and blocks the top of it from further modules.

Hussar
The Hussar Bay is a 3x2 module. It is external (no armor bonus), but does not block further construction.

Air Hussars aren't as fancy as the planes (and may have a maximum altitude, unlike planes) but have their moments.

Bomber
The Bomber hangar is a 10x1 module. It is external (no armor bonus) and blocks the top of it from further modules.

Bombers fly back & forth over the target, bombing it repeatedly without fuel or ammunition problems. Just don't send them anywhere near a flak cannon.

Torpedo Bomber
The Torpedo Bomber hangar is a 7x1 module. As expected, it's external (no armor bonus) and blocks higher modules.

Though Torpedo Bombers need to land & reload after every attack (and draw ammunition from ammunition stores! have one nearby) their straight-line attack trajectory can keep them out of flak cannons' firing arcs. They're generally a safer, if slower and significantly more expensive, alternative to Bombers.