As a candidate waveform for next-generation wireless communications, generalized frequency division multiplexing (GFDM) features several decent properties which make it promising. In this paper, we systematically overview the research about GFDM. We start with GFDM transceivers with their main components, which consist of prototype filter design, low-complexity transceiver implementation, and symbol detection algorithms. Then, we investigate a couple of non-ideal issues of GFDM, including synchronization issues, channel estimation, and in-phase/quadrature (I/Q) imbalance compensation. Lastly, we study the applications of GFDM-based cognitive radio and full-duplex radio which boast of a high spectral efficiency.