Abstract: A quantum system is said to be many-body localized (MBL) if it remains close to its initial state, i.e., it fails to thermalize. In 2016, I published a proof that certain one-dimensional spin chains have an MBL phase (the proof depended on a certain assumption on level statistics). Some recent numerical studies have raised questions about whether there is a true MBL phase. I will attempt to summarize the issues raised, but the fact remains that the mechanisms for the breakdown of MBL phase are well understood theoretically. In recent work with Morningstar and Huse (PRB, 2020), we develop specific RG flow equations. These are similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences that place the MBL transition in a new universality class.