21 cm cosmology – the concept of using radio telescopes to observe the highly redshifted 21 cm line of neutral hydrogen on cosmological scales – is a field with tremendous scientific potential. The technique, however, is faced with a significant challenge: the need to recover a very faint signal behind a sea of foreground emission nearly five orders of magnitude stronger. A first generation of 21 cm cosmology experiments that targeted observations of the cosmological Epoch of Reionization are effectively complete and, although they did not deliver a first detection of the hydrogen signal, they provided critical testbeds for developing techniques to address the challenges inherent in these observations. In this talk, I will describe the currently operating second generation of experiments in this field (including the MWA Phase II and HERA) as well as some of the associated data analysis techniques that have led to the state of the art experimental results. I will conclude by discussing what I consider to be the most difficult challenges still remaining and the most promising paths forward for addressing them.