  Stars consume hydrogen in their interiors but, generally speaking, their
surfaces continue to contain some 70% hydrogen (by mass) throughout their
lives. Nevertheless, many types of star can be found with hydrogen-deficient
surfaces, in some cases with as little as one hydrogen atom in 10 000. Amongst
these, the luminous B- and A-type extreme helium stars are genuinely rare; only
~15 are known within a very substantial volume of the Galaxy.
  Evidence from surface composition suggests a connection to the cooler R CrB
variables and some of the hotter helium-rich subdwarf O stars. Arguments
currently favour an origin in the merger of two white dwarfs; thus there are
also connections with AM CVn variables and Type Ia supernovae. Pulsations in
many extreme helium stars provide an opportune window into their interiors.
These pulsations have unusual properties, some being "strange" modes, and
others being driven by Z-bump opacities. They have the potential to deliver
distance-independent masses and to provide a unique view of pulsation physics.
  We review the evolutionary origin and pulsations of these stars, and
introduce recent progress and continuing challenges.
