I have a rather straightforward and perhaps somewhat naive question: Is there a Teichmüller theory for open surfaces?

My motivation basically is that I would like to find out more about the "space" of (almost) complex structures on open smooth orientable surfaces $\Sigma$. (For example, I learned the other day from Moishe Kohan the elementary, but nevertheless amusing fact that every orientable smooth surface admits an (almost) complex structure, hence at least two different.)

But from what I've been able to skim through the literature, it appears that most sources focus on the compact case (perhaps for a good reason?).