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In this brief survey we outline the recent advances on the stability issues of certain finite time type II blow-up solutions for the energy critical focusing wave equation in . Hereafter we use the convention . The objective of this article is twofold: firstly we describe the construction of singular solutions contained in \cite{krieger2009slow} and \cite{krieger2014full}, and secondly we undertake a detailed analysis of its stability properties enclosed in \cite{krieger2017stability} and \cite{krieger2017optimal}.