Armour serves two purposes, as does most clothing: protection and fashion. On stage and in film, if you can see the armour, it's for fashion, and if you can't, then it's for protection.
The Illusion of Practicality
From the blindingly reflective plate on Zeus to the leather scraps on orcs, armour should match the character who wears it. A good costume designer thinks about where the clothing came from, what function it supports, and how it fits with the needs of the actor and the scenes.
As for designs, there are historical examples in the Academie Duello library (which I highly recommend to learn about anything martial), and easy searches online.
Special Considerations for Lady-Parts?
First, the re-enactment to get the message: Click for hilarious video
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Here is an excellent article about the design of armour for women, from an actual armourer, that considers fantasy and practical angles. And here's a blog devoted to the same: Women Fighters in Reasonable Armour
And Other Creatures?
The current movie War Horse is set in WWI, but the use of horses in war obviously goes back to the first domestication of that animal. And many cultures protect their horses with barding. I'll leave that to Jennifer and our other equestrian experts.
But my inspiration for today's blog is this:
Take a moment to visit this awesome art project: Jeff de Boer's Armour for Cats and Mice
Hiding a Carapace
We humans, unlike our crustacean friends, are squishy on the outside, so we don armour over vulnerable parts when we have reason to believe we'll be in danger.
Stunt performers often use armour under their clothing to be able to fall down stairs, break lumber across the back, or just take a beating. This is an element of stage combat, but one we don't discuss much. If you have proper equipement, you don't need much technique or skill.
Acting Means Action
Whether in shiny plate armour or hiding kneepads under your pants, the actor needs to move and play their character. The essential consideration from a design and performance perpective is whether the actor is impeded and how much.