  The creation of carbon and oxygen in our universe is one of the forefront
questions in nuclear astrophysics. The determination of the abundance of these
elements is key to both our understanding of the formation of life on earth and
to the life cycles of stars. While nearly all models of different
nucleosynthesis environments are affected by the production of carbon and
oxygen, a key ingredient, the precise determination of the reaction rate of
12C(a,g)16O, has long remained elusive. This is owed to the reaction's
inaccessibility, both experimentally and theoretically. Nuclear theory has
struggled to calculate this reaction rate because the cross section is produced
through different underlying nuclear mechanisms. Isospin selection rules
suppress the E1 component of the ground state cross section, creating a unique
situation where the E1 and E2 contributions are of nearly equal amplitudes.
Experimentally there have also been great challenges. Measurements have been
pushed to the limits of state of the art techniques, often developed for just
these measurements. The data have been plagued by uncharacterized
uncertainties, often the result of the novel measurement techniques, that have
made the different results challenging to reconcile. However, the situation has
markedly improved in recent years, and the desired level of uncertainty, about
10%, may be in sight. In this review the current understanding of this critical
reaction is summarized. The emphasis is placed primarily on the experimental
work and interpretation of the reaction data, but discussions of the theory and
astrophysics are also pursued. The main goal is to summarize and clarify the
current understanding of the reaction and then point the way forward to an
improved determination of the reaction rate.
