The Greyhound is what is referred to as a sighthound. They are extremely fast, highly prey driven dogs that were bred to chase small game that come into their line of sight--thus the term 'sighthound'! That is why they are used for racing and trained to chase a lure.
Many people believe that due to their breeding Greyhounds cannot be reliably trained to come back. While it can be more difficult to teach a Greyhound "recall", many owners successfully teach their dogs to come when they are off leash. Although this may be a challenge it is well worth it, as your Greyhound needs exercise and there is no way you are going to be able to run as fast as your quick canine! Allowing off-leash exercise to your dog will allow him the exercise and freedom he needs. Being able to get your Greyhound to come back when called will give you the peace of mind you need to ensure his safety, and that you go home with the same number of pets you left with!
Greyhounds can make very loyal, loving pets, and teaching them to come to you may not seem difficult at first, if you are in your home or fenced yard, or in an area free from distractions. The problem arises when you encounter small prey animals, cats, and other dogs. Then your Greyhound can quickly become fixated and suddenly deaf to your calls. Training your Greyhound a reliable 'come back' command is vital for his safety, so he does not run away and get lost or worse, run into a hazard like a busy roadway with traffic. To train your Greyhound to come back you need to train him to focus on you, not every moving critter that comes along. Training on and off-leash in controlled areas like large fenced yards or dog parks during off hours to achieve this focus, before exposing your dog to open areas where distraction and encounters with other animals are likely to occur, is an important step.
While training your Greyhound to come back you are going to need to ensure his safety. Because he is so highly prey driven, and because Greyhounds can be easily startled and gone in a flash, you will need to take precautions not to lose control of your speedy friend during training. Use a well-fitted harness with a secure long line, not a retractable line. Have high value treats available, or favorite toys to reinforce “come back” and work in a safe area, free from distractions, such as a fenced yard or even a large room in your house if necessary. You may be able to use a fenced dog park during off-peak hours to train, when other dogs are not present.