In essence all ships, whether they move on air or water, depend on Archimedes's Principle: that any body submerged in a fluid is subjected to an upward force equal to the weight of the displaced fluid. Or, mathematically:
The buoyant force equals the density of the fluid times the volume of the body. A ship is an object that has a positive buoyancy, or experiences a buoyant force greater than its weight.
Before discussing further the principles of airships it is worth looking at the different classifications of airships. Conventionally all lighter-than-air craft can be divided into two categories: balloons and dirigibles. Both typically consist of an envelope containing a lighter than air gas.
Balloons float through the air with little to no control system. Most balloons intended for manned flight use hot air to rise. These vehicles have control only of their altitude, by altering the temperature and thus density of the air contained in their envelope. All other motion is dictated by prevailing weather.
Dirigibles move with direction through the air with the benefit of some on-board propulsion system. Nearly all dirigibles use rotors or propellers to move forwards with tail fins to control direction. Dirigibles with a flexible exterior are known as blimps. Rigid dirigibles are often called Zeppelins.
The term Zeppelin is an instance of brand generalization. The first practical airships were designed in Germany by Count Von Zeppelin, who had founded the world's first airline while the Wright Flyer was still struggling to get off the ground. Zeppelin's designs became the foundation of all early 20th century airships. These vehicles used a rigid skeleton with a canvas frame, protecting hydrogen or helium gas bladders.
Despite their early popularity, Zeppelins have since fallen out of use in favor of blimps. Blimps use a flexible envelope containing helium and a second air bladder contained inside. By adding or removing air from this second bag some control over the airship's density can be achieved. The high cost of helium prevents venting of lifting gas, as was done on early hydrogen airships. Hydrogen is not used any longer due to its high flammability.
Airships are seldom used now except advertising and domestic surveillance applications, where their ability to remain in one place for long periods is a necessity. They are often considered too slow for passenger or cargo applications, but this is not the primary reason they are seldom used. Instead airships are extremely dangerous when close to the ground. Because helium is too expensive to be released airship envelopes remain fully inflated even when berthed. This means that the airship is always lighter than the air and is pulling up on its tethers.
Bringing the ship in is extremely difficult under this condition and requires a large number of ground staff. No method has been found better than Von Zeppelin's original method, which involved dozens of ground crew with mooring ropes walking the airship into a hanger. This is difficult and dangerous for all involved. Lacking a hangar the airship must be tethered to a grounded mooring mast so it doesn't blow away, and can still blow over without a second mast to straighten it.
Take off is equally difficult under these conditions. A fully loaded airship may require its fins for stabilization, which means that when stationary it is impossible to control. The pilot must begin moving forward as soon as possible so the ship can be directed. Until the ship is safely in the air or has gained reasonable speed stray winds can prove deadly.
Ships that can directly control their weight by relieving lifting gas when not needed can overcome these difficulties. Landing a vehicle that weight slightly more than the surrounding air would be far easier and safer. However venting helium would be too expensive for any practical use. Hydrogen is cheap and abundant, but too dangerous to be used in a modern airship. A vacuum airship has the potential to overcome these difficulties.