When the first galaxies emerged, ~100 – 500 million years after the Big Bang, their starlight likely reionized and heated the intergalactic hydrogen that had existed since cosmological recombination. Much is currently unknown about this process, including what spatial structure it had, when it started and completed, and even which sources drove it. Recent observations of high-redshift quasars show large-scale spatial variations in the opacity of the z~5.5 intergalactic medium to Lyman-alpha photons. These spatial variations grow rapidly with redshift, far in excess of expectations from previous empirically motivated models. I will discuss possible explanations for the excess, as well as what they imply about the reionization process.