The Development of Head Defense
One of the most significant developments leading into the fourteenth century was in the way of helmets. Compound curves were used in forging to create full face helms with a near point at the top, to provide an amazingly effective surface to glance away the blows from various weapons such as the sword and the battle axe.
Of course, these full face "Great Helms" were rather large and unwieldy, and were often worn over a second small basinet (a skullcap style helm) for further protection. Most of them only weighed perhaps five or six pounds, but still - limited breathing and the limited motion allowed by them demanded that some replacement was in order.
Obviously, it would've been a step in the wrong direction at this point, to exclusively go back to the lightweight open faced kettle hats used before. As early as 1300, manuscripts showed illustrations of the earliest helms with pivoted visors - regrettably, none of them survive to this day. There are plenty of later century examples though, most notably the visored basinets.
There were two main varieties of these helms: First, and most common, was the atrociously ugly pigface basinet. It was considered to be the archetypal fighting helmet. Everyone has seen one of these, though they've probably not heard the name - this is the helm with the slightly pointed top, and the top-pivoting visor that comes to a severe point in the front, the "snout" of the helm covered in breath holes beneath the eye slots.
Much the same way that the pointed tops on helms served to provide a perfect glancing surface, so did the pointed nose of the pigface helm. Because of this, as well as because of the small eye slots, these helms are almost ideal for jousting, save one detail - the visor is held in place by leather strapping, rather than a metal latch of any sort.
Second, and much less well known, was the Klappvisor basinet. As the name might suggest, this was something that found life in the German school of armouring. Much like the pigface, the klappvisor had a top-pivot visor, and it also closed with leather strapping. Unlike the pigface, however, it was a rounded face helm. Obviously, it would've been catastrophic to take a hit directly to the face with something like a lance in one of these helms. It was a foot soldier's helm, through and through.
Both versions of the basinet were meant to be worn with a sort of fan shaped chainmaille skirt around the bottom for rudimentary neck defense. Generally held in place by leather straps attached to metal pegs called vervells, this skirt was called an aventail. At a glance it wouldn't appear to have much defensive ability, until you consider that even something as light as chainmaille could be the deciding factor in deflecting just enough of a sword's blow to keep a wound from being fatal.
As for our old friend the Great Helm, these were still being worn on occasion - however, their use was generally confined to the tournaments which were coming more and more into favor as entertainment. Most great helms were intended to be attached to the body armour, usually by way of a toggled chain or a ring hanging from the helm, and some kind of latch or hook used on the breast and back plates.
The great helm was notable in that it was used as a way to display elaborate crests, in order to identify the wearer. These were most often constructed of cuir boulli leather, or whalebone and parchment. This was a holdover from the thirteenth century, and were at least the same color as the principle charge of a knight's coat of arms, if not the same sort of creature.
As far as helms worn by common soldiers, there was still the classic open-faced kettle hat mentioned previously, worn over a simple chainmaille coif. Even this simplest of helms evolved in this time, from the "spangenhelm" construction of numerous overlapped plates, to a more sturdy design made up of two or rarely three pieces at the most.