ARC __bridge modifiers demystified

I was asked recently by one of my friends about the new bridge modifiers that became active under ARC. He asked me if I knew which ones to use in specific times and what the difference between the different __bridge modifiers were. He asked me,"so how do they work, when do I use them, how do I use them , and how do they work "under the hood" "?

Note: This was supposed to be a "Share your knowledge" type of question, where I answered the question myself, but I'm not sure I set it up properly.