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 the 1960s, 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, the speaker will discuss recent progress on spontaneous symmetry breaking in nonrelativistic system and dissipative open systems.