Space observations of magnetic reconnection indicate a variety of plasma wave modes and structures in the vicinity of the electron diffusion region including electromagnetic whistler waves, quasi-electrostatic whistler waves, electron phase-space holes, double layers, electron acoustic waves, lower hybrid waves, upper hybrid waves, and electromagnetic drift waves. These waves and plasma structures are seen in magnetotail reconnection and subsolar reconnection. The MMS mission has the unique ability to unequivocally identify the electron diffusion region and distinguish waves in the EDR from those in the extended separatrix. Such a distinction is critical since some of the observed waves may be involved the reconnection process while others may result from subsequent or associated events and do not directly influence the reconnection process. For example, some of the largest amplitude (> 100 mV/m) electrostatic waves have been identified as electron acoustic waves and upper hybrid waves. These waves are likely generated as a result of reconnection and do not appear to strongly influence the reconnection process. On the other hand, large-amplitude electrostatic whistler waves have been observed very near the X-line, are seen in simulations, and may be participating in reconnection physics. Electromagnetic drift waves almost always appear in cases of asymmetric reconnection and may lead to a more turbulent process. We summarize wave observations by MMS and discuss the relative their possible role in magnetic reconnection physics, concentrating on recent magnetotail observations.