In this talk, I will talk about the positive mass conjecture, which, roughly speaking, asserts that the total mass of an isolated physical object with positive local energy density must be nonnegative. I will begin with the ADM formalism in general relativity and the history of positive mass (energy) conjecture. Then, I will mainly discuss two different proofs of the conjecture by Yau and Schoen (1979, for n=3) and by Witten (1981, for spin manifolds). Time permitting, I will talk about its application and its recent progress.