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 Lyα line emission. However, neutral intergalactic gas that existed during the EoR was opaque to Lyα 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 Lyα flux from background galaxies. Interestingly, a 'sudden' reduction in the observed Lyα flux has now been observed in galaxies at z > 6. This review contains a detailed summary of Lyα radiative processes: I describe (i) the main Lyα emission processes, including collisional-excitation & recombination (and derive the origin of 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) reionisation and post-reionisation. 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 reionisation 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 Lyα emitting galaxies as a probe of the EoR.