A very interesting sub variation is 6...Bb6, discussed by Glenn Flear in Dangerous Weapon 1.e4 e5.
Here is the sample game :
Be6-c8-b7, u enter Arkangelsk with 2 tempi down, unlikely to be a good manoeuvre...
Moreover, In your main variation, 9.Re1 is somewhat useless because Nxe4 not a threat, indeed Nxe4 Bd5 forking!
So the move is 9.d4 instead... And now i stop because its big theory and we could talk about it many hours...
The ruy lopez(spanish) opening has been played thousands of times over the time and it can create a good advantage for white.
There are many ways that black can play to fight that.
My favourite is the Moller defense, that can give an equal or better position.
Let's take a look at some sharp lines and examples.
Hope you got something out of that cya ! :)