Measurement of the spatial distribution of neutral hydrogen via the redshifted 21 cm line promises to transform our knowledge of the Epoch of Reionization (EoR). In my talk I will give an accessible introduction to this new field, discuss how we plan to observe the faint 21 cm fluctuations in the face of strong foregrounds, and show our latest results from early observations with the MWA as we start to peer through the EoR window with the first generation of 21 cm Cosmology observatories.