I will review Penrose's singularity theorem 1965. In the theorem, the existence of a trapped surface(TS) is assumed. However, if cosmic censorship conjecture holds, trapped surface is in black hole region, that is, we cannot observe it. Therefore, it is nice to replace TS by another observable object. One of the candidates is loosely trapped surface(LTS) we proposed in 2007. I will shortly examine the relation between TS and LTS to reformulate the singularity theorem.