Recent observations paint a complex picture of the reionization of hydrogen in the intergalactic medium, with large-scale inhomogeneities and non-trivial time evolution. Unfortunately, the physical processes behind this complexity are essentially unconstrained at present. I will describe how we can study these mechanisms through the topology of neutral and ionized gas during reionization, and I will discuss a number of potential observational probes. The most exciting such probe is 21-cm emission from neutral gas in the high-redshift universe, and a number of efforts are now underway to observe this signal.