A small minority of retired racers have a high prey drive and need to live in homes without cats or small pets. Some greyhounds will bark at strangers, but that is usually out of excitement, not because they are aggressive. Their size may be intimidating to those who do not know them, however. Greyhounds are friendly and quiet, and not very threatening. They are among the most docile of breeds and form strong bonds with their families.
Greyhounds are as active as their owners.
Like other dogs, they enjoy a daily walk and the occasional opportunity to run, unleashed, in a completely enclosed area such as your backyard or a sports field. As racers they are sprinters and will need time to build up endurance for longer distances, just like people do. Only in completely enclosed areas. Otherwise, the greyhound should never be allowed to run off-leash. The risk of injury or loss of the greyhound is just too great.