I promised I'd talk about the "Airs Above The Ground" - so I will. The airs above the ground are not seen in modern dressage, but are retained by the classical school. There are seven different airs above the ground, all of which are based off of offensive or defensive cavalry maneuvers.
So I'm going to start with the pesade, which is the first of them a horse is taught.
The pesade is quite simply rearing on command, as shown here:
(Image source: Hackmann via Wikipedia Commons). The spectacular spotted horse is not an Appaloosa, but a Warmblood breed called the Knabstrupper.
Although it's not always called that, the pesade is often seen in trick riding and performed by movie horses. A fighting horse would be able to strike an opponent with the front hooves from this position. Or simply intimidate them into giving up.