From 1980’s, the study of Kleinian groups has been carried out in the framework of the paradigm of “Thurston’s problems”.

Now they are all solved, and we can tackle deeper problems; for instance to determine the topological types of the deformation spaces or to study what lie outside the deformation spaces.

In this talk, I will survey how Thurston’s problems were solved and then recent progresses in studying the deformation spaces and the “spaces outside the deformation spaces”, including my own work with several collaborators.