IEEE 802.11ay is a standard that enables enhanced throughput for IEEE 802.11 systems operating in the license-exempt 60 GHz band. By specifying advanced physical layer (PHY) features, improved channel access, and enhanced beamforming training, IEEE 802.11ay supports a maximum data rate of 100 Gb/s, making it a standard of great interest for applications as diverse as virtual reality, high density/throughput networking, and backhaul. In this paper, we provide a description and discussion of two important beamforming training procedures defined in IEEE 802.11ay, namely beam refinement protocol (BRP) transmit sector sweep (TXSS) and asymmetric beamforming training. Because these procedures build upon concepts defined in IEEE 802.11ad, we also examine two legacy beamforming training procedures: Sector-level sweep (SLS) and BRP. PHY definitions relevant to beamforming training are also reviewed.