  Collective dynamics of many particle systems is tightly linked to their
underlying symmetry and phase transitions. Higgs and Nambu-Goldstone modes are,
respectively, collective amplitude and phase modes of the order parameter that
are widely observed in various physical systems at different energy scales,
ranging from magnets, superfluids, superconductors to our universe. The Higgs
mode is a massive excitation, which is a condensed-matter analog of Higgs
particle in high-energy physics, while the Nambu-Goldstone mode is a massless
excitation that appears when a continuous symmetry is spontaneously broken.
They provide important information on the fundamental aspects of many particle
systems, such as symmetry, phases, dynamics, response to external fields, and
so on. In this article, we review the physics of Higgs and Nambu-Goldstone
modes in condensed matter physics. Especially, we focus on the development on
the study of collective modes in superconductors and cold-atom systems.
