  The chief distinction between ordinary supernovae and long-soft gamma-ray
bursts (GRBs) is the degree of differential rotation in the inner several solar
masses when a massive star dies, and GRBs are rare mainly because of the
difficulty achieving the necessary high rotation rate. Models that do provide
the necessary angular momentum are discussed, with emphasis on a new single
star model whose rapid rotation leads to complete mixing on the main sequence
and avoids red giant formation. This channel of progenitor evolution also gives
a broader range of masses than previous models, and allows the copious
production of bursts outside of binaries and at high redshifts. However, even
the production of a bare helium core rotating nearly at break up is not, by
itself, a sufficient condition to make a gamma-ray burst. Wolf-Rayet mass loss
must be low, and will be low in regions of low metallicity. This suggests that
bursts at high redshift (low metallicity) will, on the average, be more
energetic, have more time structure, and last longer than bursts nearby. Every
burst consists of three components: a polar jet (~0.1 radian), high energy,
subrelativistic mass ejection (~1 radian), and low velocity equatorial mass
that can fall back after the initial explosion. The relative proportions of
these three components can give a diverse assortment of supernovae and high
energy transients whose properties may vary with redshift.
