@auspicious99 Most of that video was a summary of Wiles's proof, not a simplification in proof. However, the answer to the question might be two results an alternate proof of faltings's theorem and a Serre Conjecture(If there's nothing else.).

I watched that video right away. The video of Ribet explaining it was exciting. About 50 minutes into that video, Ribet was talking about Khare-Wintenberger's proof of Serre's Conjecture.