Abstract: Spontaneous symmetry breaking and the Nambu-Goldstone bosons play an important role in various areas of physics. While the Nambu-Goldstone theorem for relativistic systems was established in 1960’s, it is only recently that its generalization to non-relativistic systems has been systematically studied. For example, it has been clarified that fruitful dispersion relations appear depending on the broken symmetry algebra. In this talk, I will discuss recent progress on spontaneous symmetry breaking in nonrelativistic system and dissipative open systems.