Because of their training, some greyhounds will tend to chase and harm cats and other small animals. Others simply ignore them. As with all dogs, observation and care are necessary.
Many owners say that their greyhound gets on extremely well with their other pets.
Two thirty minute walks a day are plenty, with perhaps a run off the leash in a safe, enclosed area once a week. Many greyhounds in the USA have been adopted by apartment-dwellers. Ordinary good-quality dog food is all that's required. When you first get your greyhound, you may like to put him in a standard dog-crate for short periods so that he can get used to his new surroundings. This is not cruel, as these dogs are used to long periods in confinement in an enclosed environment.