How does league matchmaking work in ranked?

So I've been really confused on how the matchmaking actually works. The matchmaking seems quite unfair at times. My question is this: Is there any formulas or algorithms I can look at that determines the matchmaking of league? This is a weird thing to ask and I don't think anyone who doesn't work at riot has this information but I would really like to know what is really going on behind the scenes.

"The clot thickens."