  The superconducting phase of hydrogen sulfide at Tc=200 K observed by Drozdov
and collaborators at pressures around 200 GPa is simple bcc Im-3m H3S,
predicted beforehand by Duan {\it et al.}, has experimental confirmation. The
various "extremes" that are involved -- pressure, implying extreme reduction of
volume, extremely high H phonon energy scale around 1500K, extremely high
temperature for a superconductor -- necessitates a close look at new issues
raised by these characteristics in relation to high Tc. We use first principles
methods to analyze the H3S electronic structure, particularly the van Hove
singularities (vHs) and the effect of sulfur. Focusing on the two closely
spaced vHs near the Fermi level that give rise to the impressively sharp peak
in the density of states, the implications of strong coupling Migdal-Eliashberg
theory are assessed. The electron spectral density smearing due to virtual
phonon emission and absorption needs to be included explicitly to obtain
accurate theoretical predictions and current understanding. Means for
increasing Tc in H3S-like materials are addressed.
