The debate on OFDM vs. single-carrier (SC) transmission started back in the 1980s at the time of the European Digital Audio Broadcasting (DAB) and Digital Video Broadcasting (DVB) projects. The same questions arose later in wireless communications, and OFDM transmission with TDMA was adopted in the IEEE 802.11a specifications for wireless local area networks and by the WiMAX Forum for fixed WiMAX systems. Later, orthogonal frequency-division multiple access (OFDMA) was adopted by the WiMAX Forum for mobile WiMAX systems and more recently by the 3GPP for the downlink of Long Term Evolution (LTE) systems. In contrast, single-carrier FDMA was adopted for the uplink of LTE. In this overview paper, we will review these historic developments and give some recent results on OFDMA and Single-Carrier FDMA.