Cognitive radio (CR) has been recognized as future prospect for efficient and dynamic allocation of bandwidth among users of which dynamic spectrum access is an important aspect focusing on identification and opportunistic utilization of vacant spectrum in television broadcasting licensed bands, known as television white spaces (TVWS). TVWS has been selected by numerous IEEE standards spanning diverse operating zones for implementing CR technology. Specifically, we focus our attention to IEEE 802.22, IEEE 802.11af and IEEE 802.15.4m standards operating in TVWS pertaining to regional, local and personal area networks respectively. The PHY layer in each of these standards is depending on orthogonal frequency division multiplexing (OFDM) for spectrum-wise efficient communication as well as dynamic frequency allocation. Pertinent OFDM design challenges corresponding to IEEE standards in TVWS are revealed. PHY layer structure and cognitive techniques employed in cognition-aware IEEE standards in TVWS are reviewed in detail. Lastly, open research issues and implementation challenges for TVWS IEEE standards are highlighted.