Daniel covered a good amount of the history and fine points (if you'll forgive the pun). I'm just going to jump in as a martial arts fencer (as opposed to Olympic), and instructor.
What we have here is evolution at work.
The rapiers that first developed in the late 15th century were more similar to medieval style swords than their descendants. They had the thickest blades (usually and inch and a quarter in width), and were equally effective at cutting and thrusting. They had quillons that were thick, and very like earlier crosspieces. Due to the weight of the blade many early fencers gripped their forefinger over the quillon in order to have better control of their weapon, especially while thrusting. As armoured gauntlets were going by the wayside due to the introduction of firearms rings were added to protect the fingers. Eventually a knuckle bow was added, and the hand was better protected. The swept hilt developed from this.
As various nations, namely Italy, Spain, France, and Germany developed their own styles of rapier fighting they also started developing their own guards. German General Gottfried Heinrich Graf zu Pappenheim developed the style named after him: highly decorated grillwork or shells in the rings of the anneau. His blades remained thick as they were a military sword. In the late 1500s, early 1600s you see the bell shaped guards replacing the swept hilt, and quillons becoming longer. This is true mostly in Spain and France. Sadly, England got to the game late as they actually passed laws against fencing schools in the 13th century where heavier blades were preferred.
Blades thinned started thinning over time. Early rapiers were thick and mostly used for cutting like their ancestors. Most of the "standard" attacks were countered by moving, or parrying with a dagger. Then, just after 1600 Di Grassi (my hero) wrote his treatise on rapier fencing and pointed out that the thrust is the fastest way to kill the other guy, and that the best strategy to use was one where you killed the other guy first, and didn't get injured yourself. Angelo Viggiani then developing the lunge, followed by Vincentio Saviolo who went even further than Di Grassi in favoring the thrust over the cut.
Due to rapiers being used for thrusting over cutting they no longer possessed the weight to cut by percussion and began to be on average 40 inches in blade length alone. Because of this fences, when they had to cut, were using the draw cut. In order to do this properly you place your blade on your opponent and push or pull your blade. If you try and "thwack" them, your blade will use most of its energy bouncing off.
These thinner, thrusting weapons eventually started becoming smaller again as they were used more for dueling by citizenry, and not used in warfare as often. several hundred years of experimentation had made complex swordplay where the lightest, fastest possible weapon usually won. The weapon's component parts–the quillons, cup, knucklebow and pas d'âne–all shrank down to the smallest useful size. The result was the'small sword,' a weapon that eclipsed the rapier completely in the 1700s.