The Nuts and bolts

Libertarian free will - no, not like Libertarians the political party. But like "freedom". In some ways, you might say it's the purest form of free will. You've got it, you really make choices for real, and that's that.

Determinism - In a nutshell, we're all bound by the chemistry and structure of our brains, by all that sciencey stuff. THAT stuff is making the choices. You might seem like you're making choices, but you're not.

Compatiblism - This marries the two ideas. We really do make our choices, even if we're nothing but chemistry and sciencey stuff. 

For my money, compatibleism is the winner here. It doesn't matter at all, if your brain is "just" physics, "just" chemistry, "just" a hundred billion neurons capable of making more connections between themselves than there are atoms in the universe, "just" capable of feeling love, "just" able to be overcome with emotion over poetry, over reuniting with long lost friends, "just" able to ponder your hopes and dreams, "just" able to weigh information and consider outcomes that serve those dreams. Everything important about agency, about making choices shows up in that machine, because that machine itself is capable of choices, real choices. It's a choice-making engine. There's no contradiction between being built out of the stuff of physics and then as a creature of physics, gathering information, having preferences, and radiating signals out to the body to act on their choices.

I think people who favor libertarian free will have tragically shortsighted imaginations and think that they "lose" something if they concede determinism. And similarly I think determinism is a bit short sighted for thinking that such a thing as a brain can't be the kind of thing that genuinely is engaged in the process of taking the information, feeling things and making choices.

Those are the nuts and bolts.