Electrodynamics of high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>superconductors

Recent studies of the electromagnetic response of high-${T}_{c}$ superconductors using terahertz, infrared, and optical spectroscopies are reviewed. In combination these experimental techniques provide a comprehensive picture of the low-energy excitations and charge dynamics in this class of materials. These results are discussed with an emphasis on conceptual issues, including evolution of the electronic spectral weight in doped Mott-Hubbard insulators, the $d$-wave superconducting energy gap and the normal-state pseudogap, anisotropic superfluid response, electronic phase segregation, emergence of coherent electronic state as a function of both temperature and doping, the vortex state, and the energetics of the superconducting transition. Because the theoretical understanding of these issues is still evolving the review is focused on the analysis of the universal trends that are emerging out of a large body of work carried on by many research teams. Where possible data generated by infrared/optical techniques are compared with the data from other spectroscopic and transport methods.