As pointed out by Nambu-Goldstone theorem, the breaking of continuous symmetry gives rise to massless or gapless bosonic excitations. In superconductors, continuous local U(1) gauge symmetry is broken. The gapless excitation thus created is the collective phase mode of the superconducting order parameter. In 1962, Philip Anderson pointed out that the Coulomb interaction between Cooper pairs lifts this gapless mode to the superconducting plasma frequency. Therefore, in a superconducting fluid there are no bosonic excitations below the binding energy of the Cooper pairs (2Δ). Anderson’s mechanism also implies that the massless photon, which mediates electromagnetic interaction, becomes massive in a superconductor. This mechanism provides a microscopic theory for the dissipationless charge transport (in conjunction with Landau’s criterion for superfluidity) as well as the Meissner effect inside a superconductor. Jumping into particle physics, in 1964 in order to explain why the gauge bosons for electroweak interaction, namely the W±, Z bosons, are massive, Peter Higgs, François Englert, Tom Kibble and colleagues proposed the existence of a field (presently referred to as the Higgs field) in nature. This matter field couples to the massless W±, Z bosons and generates mass via the Higgs mechanism. Due to their conceptual similarities, these two mechanisms are collectively referred to as the Anderson-Higgs mechanism nowadays. In 2013, the scalar excitation of the Higgs field, namely the Higgs boson, was detected at the Large Hadron Collider, providing the final proof for the Higgs hypothesis nearly 50 years after its proposal. The amplitude mode of the superconducting order parameter, which corresponds to the Higgs boson through the above analogy, is referred to as the Higgs mode of a superconductor. Its spectroscopic detection has also remained elusive for nearly half a century. In recent years, the development of ultrafast and nonlinear spectroscopic techniques enabled an effective approach for investigating the Higgs mode of superconductors. In this paper, we will introduce the historical background of the Higgs mode and review the recent developments in its spectroscopy study. We will also discuss the novel perspectives and insights that may be learnt from these studies for future high-temperature superconductivity research.