Here is an excellent article on the use and abuse of greyhounds in dog racing. The article is about the UK, but this is a worldwide problem.
From the article about the Greyhound Derby at Wimbledon:
The elite - dogs like Westmead Lord, hot favourite for the derby - are the lucky few. At the end of their careers, they'll be put out to stud.
As for the rest - the majority - a short, miserable life will be followed by a brutal and needless death.
Most will suffer a fate similar to those buried in a "mass grave" next to David Smith's bungalow off a secluded farm track in County Durham.
The method of execution for those unfortunate animals was a bolt gun, a weapon that fires a metal bar with enough force to shatter the toughest skull.
This is a lot cheaper than finding them new homes. It didn't take much for an animal to be discarded. Said one former trainer:
"The person I worked for was only interested in making money out of his dogs. Once a dog could no longer race, he wanted rid of it.
"I was very attached to one particular greyhound and walked him for a year. I was hanging on in the job waiting to adopt him when he retired. But it wasn't to be.
"The dog's shoulder was shattered in a race. Afterwards, the head kennel hand came back holding the dog's lead. I asked where the dog was. She just said 'get on with your work. This became a familiar pattern."
Greyhound Action (mentioned in the article) has a good website with information.