The IEEE 802.11 standard has rapidly become the de facto standard for Wireless Local Area Networks (WLANs) under the commercial name Wi-Fi. Despite IEEE's regular efforts to improve the energy efficiency of Wi-Fi, many energy-saving mechanisms remain relatively unknown to the community, which contributed to hamper their large-scale adoption by chipset manufacturers. In this paper, we describe the main MAC mechanisms that have been introduced by the IEEE 802.11 standards (and its amendments) for the sake of saving energy. This includes diverse mechanisms where either the stations (STAs) prompt the access point (AP), the AP notifies the STAs, or the STAs and the AP make an appointment. In every case, we illustrate the mechanism's principle through examples. We also present a set of metrics to compare the effectiveness of energy-saving mechanisms with each other and discuss how the energy-saving mechanisms of IEEE were adopted by the Wi-Fi Alliance, and hence by chip manufacturers. Overall, we believe that this paper, which accurately details these mechanisms, can help researchers, manufacturers, and network operators to have a clear understanding of what Wi-Fi is readily capable of doing when it comes to energy efficiency, and thus foster their use in actual and upcoming WLANs.