Appears in collection : Not Only Scalar Curvature Seminar

The positive mass theorem of Schoen-Yau and Witten is one of the most important results about scalar curvature. It is intimately connected with the existence of positive scalar curvature metrics. Various motivations lead to consideration of singular metrics. In this talk I will survey some recent results of many people along this direction and present our recent work with Yukai Sun and Changliang Wang for isolated conical singularity.