Green radios jointly consider the spectrum efficiency and the energy efficiency in wireless networks in order to provide sustainable development. In the past two decades, various green radio solutions for different types of terminals and radio access networks have been developed, some of which have been used in the designs of wireless products. In this paper, we provide a historical view on some fundamental works and practical issues. In addition to providing a comprehensive overview on theoretical achievements, we also discuss several important power saving solutions with notable engineering impacts, such as Doherty power amplifier and separated baseband unit - remote radio unit architecture, which might be overlooked in previous publications. Moreover, with the huge growth of wireless traffic in the near future, green radio design for future wireless networks shall involve an end-to-end energy efficiency investigation of mobile terminals, radio access and core networks, and different applications. By introducing green radio schemes for advanced terminals and future wireless networks, this article will not only be beneficial for readers with only preliminary background in communications and signal processing but also have reference and historical values for researchers and practical engineers in the area.