  Extremely hot horizontal branch (HB) stars and their progeny are widely
considered to be responsible for the "ultraviolet upturn" (or UVX) phenomenon
observed in elliptical galaxies and the bulges of spirals. Yet, the precise
evolutionary channels that lead to the production of these stars remain the
source of much debate. In this review, we discuss two key physical ingredients
that are required in order for reliable quantitative models of the UV output of
stellar populations to be computed, namely, the mass loss rates of red giant
branch stars and the helium enrichment "law" at high metallicities. In
particular, the recent evidence pointing towards a strong enhancement in the
abundances of the alpha-elements in the Galactic bulge (compared to the disk),
and also the available indications of a similar overabundance in (massive)
elliptical galaxies, strongly suggest that the helium abundance Y may be higher
in ellipticals and bulges than it is in spiral disks by an amount that may
reach up to 0.15 at [Fe/H] ~ +0.5. If so, this would strongly favor the
production of hot HB stars at high metallicity in galactic spheroids. We also
discuss the existence of mass loss recipes beyond the commonly adopted Reimers
"law" that are not only more consistent with the available empirical data, but
also much more favorable to the production of extended HB stars at high
metallicity. Finally, we discuss new empirical evidence that suggests that
different evolutionary channels may be responsible for the production of EHB
stars in the field and in clusters.
