Woodin, W. Hugh. 2017. “In Search of Ultimate-L the 19th Midrasha Mathematicae Lectures.” The Bulletin of Symbolic Logic 23 (01) (March): 1–109. doi:10.1017/bsl.2016.34.
We give a fairly complete account which first shows that the solution to the inner model problem for one supercompact cardinal will yield an ultimate version of L and then shows that the various current approaches to inner model theory must be fundamentally altered to provide that solution.