Deerhounds were bred in parallel with the Greyhound for very similar purposes. They were developed to hunt deer by running them to ground (exhaustion) in packs. As such, they are very closely related to the Irish Wolfhound, Russian Wolfhound, and the other large sighthounds. Generally, these big hunting dogs were sporting animals for nobility but many very similar animals were bred and hunted by common folk. These big, fast, almost silent hunters made quick work of any game from a rabbit up and were very well regarded by noble huntsmen and poachers alike.
The Deerhound is a large dog that needs quite a bit of exercise to keep it healthy. That does not mean it needs a large house to live in. Many live in smaller houses and apartments quite happily. The average adult Deerhound (over, say, two years old) spends much of the day stretched out on the floor or a couch, sleeping. They are gentle and docile indoors and are good around company and children.
Outdoors, with room to run, they are anything but docile. It is a joy to watch Deerhounds loose running around for the sheer joy of it. They have a long floating gait and are amazingly fast over a piece of ground. Some care has to be taken to give them freedom to run in places where they are not likely to be tempted or able to give chase as they are tireless runners and fierce hunters.
Deerhounds compete in conformation and coursing. Many are trained to succeed in obedience competition but few excel in it and fewer excel in dog agility or flyball.