  The Epoch of Reionization (EoR) represents a milestone in the evolution of
our Universe. Star-forming galaxies that existed during the EoR likely emitted
a significant fraction (~5-40%) of their bolometric luminosity as Lyman Alpha
(Lya) line emission. However, neutral intergalactic gas that existed during the
EoR was opaque to Lya emission that escaped from galaxies during this epoch,
which makes it difficult to observe. The neutral intergalactic medium (IGM) may
thus reveal itself by suppressing the Lya flux from background galaxies.
Interestingly, a `sudden' reduction in the observed Lya flux has now been
observed in galaxies at z >6. This review contains a detailed summary of Lya
radiative processes: I describe (i) the main Lya emission processes, including
collisional-excitation & recombination (and derive the famous factor `0.68'),
and (ii) basic radiative transfer concepts, including e.g. partially coherent
scattering, frequency diffusion, resonant versus wing scattering, optically
thick versus 'extremely' optically thick (static/outflowing/collapsing) media,
and multiphase media. Following this review, I derive expressions for the
Gunn-Peterson optical depth of the IGM during (inhomogeneous) reionization and
post-reionization. I then describe why current observations appear to require a
very rapid evolution of volume-averaged neutral fraction of hydrogen in the
context of realistic inhomogeneous reionization models, and discuss
uncertainties in this interpretation. Finally, I describe how existing &
futures surveys and instruments can help reduce these uncertainties, and allow
us to fully exploit Lya emitting galaxies as a probe of the EoR.
