I don’t think anyone has yet brought up the Lurcher. This is neither a breed, nor a particular cross of breeds, but is a “type” of crossbreed that has existed for hundreds of years, bred not for the pet market, but for a particular hunting niche. Originally, this cross of a sighthound (greyhound, whippet, Saluki, borzoi, Irish Wolfhound,Scottish Deerhound most commonly) crossed with a collie breed (border collie or bearded collie most often) or terrier ( most often Bedlington or Staffy Bull) was often used for poaching or other illegal in the UK hunting activities. It was associated with Gypsies although that may not be accurate.
This cross was desired because it combined the predatory speed and desire of the sighthound with the more biddable nature of the sheepdog, I suppose terriers are more biddable than sighthounds, but for sure, sighthounds are always very silent hunters which was desirable in this situation.
Lurchers are still being bred in the UK and in the US- they can be wonderful companions and were some years ago prized by the “horsey set” - think there was one in the Jilly Cooper book “Riders".
But, lurchers are a type, or cross, not a breed. Sometimes the F1s are bred on, to what depends on what is desired as far as hunting.
I must confess a friend friend of mine who breeds top class greyhounds and I did consider an Irish Wolfound x Greyhound cross (A sighthound x sighthound cross is called a Longdog, while a deerhound or Wolfhound x greyhound is called a Staghound). Both the individuals we were thinking of were champions who had passed all their breed health testing, but it was their characters as well as their conformation that tempted us. In the end, we felt that we would each like two puppies from this breeding, but if she had twelve, we weren’t certain we could provide appropriate homes for the puppies.
We have sometimes wished we had gone ahead and done it!
I once went to a Luncher show in Ireland. I had no idea how they might possibly judge such dissimilar looking animals but each pair was quite similar and you could sort of make sense of it.