  In this paper, we explore the constraints on the reionization history that
are provided by current observations of the Lyman-alpha forest and the CMB.
Rather than using a particular semi-analytic model, we take the novel approach
of parametrizing the ionizing sources with arbitrary functions, and perform
likelihood analyses to constrain possible reionization histories. We find model
independent conclusions that reionization is likely to be mostly complete by
z=8 and that the IGM was 50% ionized at z=9-10. Upcoming low-frequency
observations of the redshifted 21 cm line of neutral hydrogen are expected to
place significantly better constraints on the hydrogen neutral fraction at
6<z<12. We use our constraints on the reionization history to predict the
likely amplitude of the 21 cm power spectrum and show that observations with
the highest signal-to-noise ratio will most likely be made at frequencies
corresponding to z=9-10. This result provides an important guide to the
upcoming 21 cm observations. Finally, we assess the impact that measurement of
the neutral fraction will have on our knowledge of reionization and the early
source population. Our results show that a single measurement of the neutral
fraction mid-way through the reionization era will significantly enhance our
knowledge of the entire reionization history.

Cosmology and Nongalactic Astrophysics