Sword blades are generally made out of the toughest metal available. In antiquity, this was copper, then bronze. Once iron was discovered, that was used and finally steel. Prior to the invention of steel, several techniques were developed for reducing the brittleness of the iron. Perhaps the most well-known is pattern welding. This was a very labour-intensive technique - and so such swords were very expensive.
Various techniques were also employed to make the blade harder. In particular, case hardening (also known as Differential hardening) was popular - the sword was heated up and plunged into water. The outer layer of metal was thus made very hard but brittle, inner layers hopefully retaining some toughness to counteract the brittleness.
Decoration was often applied to the blade - usually engraving and sometimes inlaying with gold. In the 19th century it became common to etch designs on the blade using acid and a wax template.
Swords may have either a straight blade or a curved one. A straight sword was primarily intended for stabbing, whilst a curved sword was intended for slashing.
Stab wounds were more lethal, and so straight swords were generally preferred, at least by infantry.
For a horseman, stabbing was not practical because it is hard to make a horse move swiftly backward should the thrust fail to strike the victim. The cavalryman would then be at the mercy of his erstwhile victim. This was not so important in massed cavalry charges, in any case in such attacks the cavalry would often be in closely packed formations in which slashing would not be possible. Consequently European heavy cavalry generally had straight swords.
Cavalry which engaged in single combat or in looser formations normally had curved swords. In order to cut, a sword had to be drawn across the victim's skin, and a curved sword was more suitable for this. The blade was only sharpened on the outer edge and the a radius of curvature was equal to the distance from the centre about which the blade was rotated - i.e. the distance from the blade to the shoulder.
In European swords, this was usually a full arm's length, but in the Middle East and Indian swords it as generally a much shorted distance - typically 50 cm or so. This gave Eastern cavalry a great advantage over their European counterparts because they were able to fight at a closer distance than the Europeans were used to and therefore get inside their sword arc.
Single-edged swords have a back. This is the unsharpened edge. Early 19th century swords had a "pipe-backed" appearance, whereby they had a thickened ridge along the back to make the blade stronger.
As the 19th century progressed and metallurgy improved, pipe backs were no longer necessary. They gave way to grooves cut in the side of the sword and these were known as "fullers". As well as making the sword lighter, they made it more flexible and less likely to snap.