Street cats...

I have always been a dog lover, and slightly scared of cats. However since moving to Turkey I have now mellowed out. It is heartbreaking to see so many cats on the street. There are thosands of street cats here and they are continually breeding. I don't know how Turkey can tackle this problem, but they have started to make steps by making it free for street cats to be neutered. A lot of people will buy cat food and leave it in public places so the cats can eat. I have a dog and I have tried to integrate a cat into our house, my dog is harmless and just wants to play, but the cats are instantly on the defensive as they are used to fighting and think dogs are the enemy. So I ave been unable to rehome one.
How do you feel about street cats? Have you any ideas on how you would tackle this problem? Would your heart melt and adopt a couple of cats?