  When a continuous symmetry of a physical system is spontaneously broken, two
types of collective modes typically emerge: the amplitude and phase modes of
the order-parameter fluctuation. For superconductors, the amplitude mode is
recently referred to as the ''Higgs mode'' as it is a condensed-matter analogue
of a Higgs boson in particle physics. Higgs mode is a scalar excitation of the
order parameter, distinct from charge or spin fluctuations, and thus does not
couple to electromagnetic fields linearly. This is why the Higgs mode in
superconductors has evaded experimental observations over a half century after
the initial theoretical prediction, except for a charge-density-wave coexisting
system. With the advance of nonlinear and time-resolved terahertz spectroscopy
techniques, however, it has become possible to study the Higgs mode through the
nonlinear light-Higgs coupling. In this review, we overview recent progresses
on the study of the Higgs mode in superconductors.
