Fantasy Armor

Oh boy...

The short version of it is that people involved in game designing (both traditional and video games) tend to design female armor to be more sexually attractive than functional. This topic can lead to lively debates.

Categorization

Here's a brief rundown...

Category Zero: A female character is simply clad in regular armor that is identical to what male characters have and is purely functional in design. If it has any ornamentation, it is simply the sort of ornamentation that is common for that region. Some examples include chainmail shirt and a helmet, a suit of plate, gear worn by modern female soldiers in combat situations, etc.
Category One: Armor is specifically made to be worn by women, but is still functional. Ornamentation, if present can be more feminine. Think of the difference between a man's and a woman's suit. Cat One armor is either as good or better for a female wearer than Cat Zero armor.
Category Two: (Boobplate) Specific to plate armor, this involves a pair of boobs being hammered into a breastplate. This will direct a sword blow (or worse: a bullet) inward towards the heart. A simple raised section in the armor to accommodate breasts would fall into Category One. Special note has to go to the real world Greek Muscle cuirass which had sculpted boob plates, only it was worn by men (ie the Sanguinary Guard), and further only by officers, making it a rare case of male category 2 or 1. That said, since a six pack and abs is flatter than a pair of boobs it's much less of an issue.
Category Three: Female armor which is really really tightly fitting, thus making it hard to put on or take off, decreasing its effectiveness as armor and making it hard to move in.
Category Four: Armor with cleavage, mid-riffs and similar, leaving portions of the body exposed for blades, spears and arrows. Also appearing at this point are high heels, and not the kind intended for riding.
Category Five: Chainmail and plate bikinis. At this point we are not dealing with armor but rather armor themed stripper costumes whose only purpose is for pure fanservice. The male example is roman gladiator armor which usually only consisted of armor on a single arm and a belt.
Category Six: Included only for completeness sake, a cat 6 is no armor and no clothing, runing into battle completely naked. This was historically done by males of certain cultures such as the Norse and Celts. Interestingly the Celts and Vikings were also known for having female warriors meaning category 1 and category 3 and 6 (more so Celts than Vikings), as none of these people used plate armor, this is the most likely option on this list for West-specific historical accuracy and "artistic license of historical events", which is kinda pathetic if you think about it. Scythians and Sarmatians would fall under category under category one.

Ubiquity

Even for all it's silliness, the bigger issue is not that this stuff exists. If it was something which cropped up once in a blue moon it would be dismissed as a quirk of a few series who are a bit more fanservice heavy than others. The real issue that it has become effectively the norm rather than the exception. That said, there has been a bit of a backlash against this in recent years.

Perspectives on Female Fantasy Armor

On the one hand you have people who are against revealing female armor. It's self evidently badly designed for the purpose of protecting it's wearer and exists for reasons of cheap fanservice. That it has been allowed to become the norm also reflects poorly on people who like the genre, making them come off as juvenile and sexist, as well as keeping away women who might otherwise be interested.

Then you have it's proponents/defenders. Said people would argue that it adds flavor to the setting and that it looks nice. When confronted with it's deficiency in terms of protection, some people will try to defend them by making points such as "women being unable to carry as much weight as men". In general terms true, but mostly this has to do with upper body strength in the arms, strength in the legs and spine is more even between individuals of both sexes of comparable size and build and armor is mostly carried by the shoulders for the same reason a backpack is, and the upper arm body strength lacking is due to social pressure not to use upper arm body strength and not biology. Another oft quoted and lacking of understanding of physics ice is "increased mobility", leaving aside the matter of high heels or the cumbersomeness of wearing an armored corset. The only fictional character who gets away with this is the current Samus, because her high heels are actually jet-heels [1] which also allows her to kick opponents in the face and burn them at the same time. The 'socially pragmatic' card is "distraction" assuming that all men are dumb and horny enough to automatically let their guards down to stare at tits, double sexism ho! Others, who realize that it's a bad design would bring up that A) The name of the genre is Fantasy and its defined by moving trees, animate statues and giant armored winged reptiles that can fly and spew fire out of their mouths without incinerating their tongue, so unrealistic elements are to be expected and B) in real life women seldom served as warriors during the middle ages in any case.

A third group exists which settles somewhere in between the previously mentioned groups. These are people who feel that it depends on the setting. If it's a setting where male and female soldiers fight in pike formations and phalanxes supported by companies of crossbow armed soldiers using volley fire, halberdiers, mounted archers and lancers and otherwise aims for a degree of realism, have reasonable and functionally designed female armor. For more overtly fantastical stuff and stuff like Conan the Barbarian where you have guys wearing a single pauldron, a bandoleer for a sword, a kilt and a pair of boots into battle, the chainmail bikinis fit the tone and are fine. Notably, Dark Sun was specifically designed as a desert world solely to make this style of armor make sense and because the developers forgot that actual desert dwellers have to wear concealing full-body outfits to prevent sunstroke.

Female Armor in Real Life

YEAH GOOD THANKS.

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Gallery

Jenette Vasquez from Aliens in Category Zero. As seen with Hudson as a comparison, her armor looks exactly like the ones male marines use (apart from the extra equipment used to allow her to use a Smartgun system).
Elspeth Tirel shows off a suit of Category One: while being without a helmet and with a flowing long robe this is the standard suit of armor for the knights of Bant, who will not exploit these two weaknesses when fighting their honorable duels.
Sister Miriya of the Sisters of Battle in Category Two. Category Two armor is generally the most acceptable form of female armor for most fantasy fans since it logically looks like it can protect the user while remaining aesthetically pleasing.
An Eldar Farseer in Category three. Although, while it is tight-fitting, Eldar mesh armor is designed to be tight while still allowing users free movement. Plus, while the picture is of a woman, Eldar men wear the exact same armor making this an out of universe type three, but in universe type two since she still has a boob plate (to clarify, male Eldar banshees are expected by Khaine to wear these too, and the other 12 Warrior Paths and Guardians completely lack it, but Autarchs and Farseers use it.)
Lelith Hesperax in a Category Four/Five Hybrid. While it can't protect her, it is nearly impossible to strike Lelith in the first place due to her borderline-supernatural agility, and so her armor is optimized to be as lightweight(and thus easy to maneuver in) as possible. Additionally, Dark Eldar culture demands that Wyches and Succubi be as sexually appealing as they are deadly in combat- a Wych that isn't attractive enough for the crowds inevitably ends up in an arena match that she can't win and the male members of wych cults dress about as skimpily.
A male category 2 muscle cuirass. It has largely the same problems as female category two. They even went to the trouble of hammering out nipples and a navel.
A male category 4/5 historical roman gladiator. The exposed chest is considered to be the gladiators badge of honor. If you've pierced that, you've pierced the gladiators honour.