becoming preferred in later ones. Crosspieces varied considerably although they did tend to get larger in the later period.
Longsword was normally used in both hands with techniques for using the point, edge, pommel and even crosspiece to strike the opponent. In early period Longswords, the edges were parallel and the sword’s point was a somewhat secondary offensive feature. At this time the sword was mostly used to hew or chop. As armour improved in protection, the chopping Longsword evolved into the thrusting B@stard sword. This was a weapon (so called as it was neither a single handed nor a true two handed sword) with an elongated isosceles triangular, rigid blade relying on the point. Using the sword in a sort of bayonet drill (left hand on the blade, right on the hilt) was popular in fully armoured combat. This allows the wielder to thrust, block or strike with the pommel with considerable power.
More details about history can be found here