One valve gear over another

I still do not really know the purpose of valve gear , I am guessing it has something to do with controlling admission of steam to the cylinders and thus applying power to the drivers.
I also know there were numerous types of valve gear, starting with the simple slide valve motion then going through the range with Stephenson, Walschaerts (sp?), Pilod-Baker, Southern, etc.
My question is what advantage was gained, and how, by using a more complicated valve gear over what had to be a simpler to maintain slide valve type set-up.
To those who understand this sort of thing, THANKS!