Structure

Lighter-than-air Aircraft are of two types--rigid airships like Zeppelins, and non-rigid airships, like blimps and balloons.  They work on Archimedes' principle; they "float" in air because they displace a volume of air whose weight is greater than the weight of the ship.

Modern airships utilize helium gas to achieve this buoyant force; it is much safer than the hydrogen gas used in the past because it isn't flammable.  In the past, hydrogen was used because helium was rare, but now Helium is widely available because it is a byproduct of natural gas production.  Hot-air balloons, of course, use hot air for lift, because hot air is less dense than cold air and will float.  The air in the balloon is heated by an on-board flame.

Gas Envelopes

The materials used today in airships' gas envelopes are highly advanced; pound-for-pound they are stronger than steel and are not damaged by ultraviolet light.

The pressure inside the envelope is extremely small (0.067 psi), so a small leak in the envelope takes a very long time to affect the airship's flight.  Inside the gas envelope, the helium expands and contract with temperature changes, so a device called a ballonet inside the envelope expands and contracts to counteract this.  As the helium expands, the ballonet released air to counteract the expansion and keep a constant pressure.

Propulsion

Airships do not require speed for lift, so they have very small propulsion systems (hot-air balloons have none at all).