Since leaky-wave antennas (LWAs) have the advantages of high directivity, low loss and structural simplicity, LWAs are very suitable for designing millimeter-wave (mmW) antennas. The purpose of this paper is to review the latest research progress of LWAs for 5G/B5G mobile communication systems. Firstly, the conventional classification and design methods of LWAs are introduced and the effects of the phase constant and attenuation con-stant on the radiation characteristics are discussed. Then two types of new LWAs for 5G/B5G mobile communication systems including broadband fixed-beam LWAs and frequency-fixed beam-scanning LWAs are summarized. Finally, the challenges and future research di-rections of LWAs for 5G/B5G mobile communication systems are presented.