Hybrids and Evolution

In this thread I want to consider the biology of hybrids. I want to do this to increase my understanding of the underlying biology of reproduction and the definition of "species".Why are hybrids such as mules and ligras infertile?
Why are hybrids even biologically possible from an evolutionary point of view?
What interesting examples of hybrids are known to exist or be possible?
How closely related do species have to be in order to successfully breed a hybrid? What do we actually mean by "closely related"? What does this mean in terms of DNA, genetics, chromosomes etc. etc.?
Where is the line that divides the ability to reproduce fertile offspring, infertile offspring and the inability to breed at all? Are there definite dividing lines or is it a graduated scale?
What does the existence of hybrids tell us about evolution as a theory?Ignoring the moral questions how feasible is a chimp-human hybrid? From a purely biological perspective how feasible is this as a physical possibility?I would prefer that this thread not be cluttered up with anti-evolutionists. Nor do I want the moral question of human hybrids to become the focus. I want to understand the pure biological science of these questions.

Good grief!Was this a natural occurrance or (as I am assuming) bred in a lab?How do we genetically account for a hybrid animal of this type that is twice the size of either of it's parent species?

I was really hoping for some serious and detailed bio tech answers to these questions. Bluejay and others have given some brief answers but surely the EvC bio contingent can provide better answers to the questions posed than have been forthcoming so far?