Can you describe the various filling mechanisms?

Piston

Here, the ink is contained within the barrel of the pen for maximum capacity. A piston knob at the end of the barrel operates the internal piston to draw ink up into the barrel via the nib, a bit lit a syringe. Examples of pens that use this system are Pelikan Souverän, Lamy 2000, Aurora Ooptima and most Bexley and TWSBI models. Piston-filling pens usually have an ink window so the user can see how much ink is left.
Pros: enormous ink capacity.
Cons: cartridges cannot be used.

TWSBI Diamond 580

Cartridge/converter

By far the most common method and used on most modern fountain pens. The user fills the pen by unscrewing the barrel and either operating a piston or squeeze "converter" to fill from an ink bottle or else simply replaces the empty cartridge. It is therefore possible to switch between using bottled ink and cartridges by removing the converter.
Pros: convenience, ease of cleaning and maintenance, use of cartridges when bottled ink is impractical (eg when travelling).
Cons: holds less ink than a piston-filling pen.

Lamy Z28 converter

Lever or button fill

A traditional filling system where the pen barrel contains a rubber sac that is squeezed either by the lever or button actuated mechanism. Examples include Conway Stewart Churchill and Duro models.
Pros: traditional look.
Cons: can't usually see how much ink is left. Maintenance, if required, can be more difficult.

Integral piston converter

A cross between piston and converter methods, for example in the Conway Stewart Winston and in some Conway Stewart 100 and Nelson models. The pen has a built-in piston mechanism but the ink is not held in the barrel.
Pros: ink is insulated from the user's hand so thermal expansion is not an issue. Easier maintenance than a piston-filling mechanism.
Cons: lower ink capacity than true piston mechanism, user can't always see remaining ink.

Vacuum filler

Vacuum or plunge fillers are unique in that they empty and fill with one stroke of the rear plunger. The vacuum filling method was developed by Onoto in the early part of the 20th century and later used by Sheaffer. Current examples include higher-end Visconti models and the TWSBI Vac 700. The system works by a partial vacuum being created behind the seal of the plunger as it is pushed down inside the barrel. This vacuum is then released as the plunger reaches the end of its travel and replaced by ink drawn up through the nib and feed. During this movement of the plunger, any ink still in the barrel is forced out through the nib and feed before the vacuum is released, therefore the pen empties and fills with one stroke. Ingenious!
Pros: enormous ink capacity (well over half the internal volume of the barrel). One-handed operation.
Cons: can be more difficult to clean out than cartridge/converter or piston systems. Technically complex.

Eye-dropper

The simplest of all filling methods. Not really a "mechanism" at all, ink is simply poured into the barrel using an eye-dropper.
Pros: enormous ink capacity - virtually the entire barrel of the pen. Very simple with no moving parts.
Cons: requires a perfect seal between the front section and barrel. Potentially messy.