The largest \(L\)-like inner models for large cardinals that have been obtained so far can contain Woodin limits of Woodin cardinals (Neeman 2002). However, building an \(L\)-like model for a supercompact cardinal is still a challenge. The supercompact barrier seems to be the crucial one, for Woodin has shown that for a kind of \(L\)-like inner model for a supercompact cardinal, which he calls the Ultimate-\(L\), all stronger large cardinals that may exist in \(V\), such as extendible, huge, I1, etc. would also exist in the model. The construction of Ultimate-\(L\) is still incomplete, and it is not clear yet that it will succeed, for it rests upon some technical hypotheses that need to be confirmed.