In order to improve the responsivity and reduce the noise equivalent power of Field-Effect Transistor (FET) THz detectors, a suitable planar antenna structure is necessary.In this paper, we investigate the research progress of FET THz detectors integrated with planar antenna structures. Firstly, we analyze the working principle of FET THz detectors and clarify that an integrated planar antenna could effectively improve the detector's performance by enhancing its coupling efficiency with terahertz waves. Secondly, we present some typical planar antennas and discuss their pros and cons. These include the dipole antenna, the patch antenna, the slot antenna, the grating-gate, and others, which are each compared with respect to responsivity for the detectors. Finally,we find that the responsivity of the FET THz detectors can be greatly improved when applying planar antenna structure and that each type of antennas contributes uniquely. This work introduces several planar antennas integrated into FET THz detectors, including the performance and research progress of various antennas.Some existing problems are described and some predictions of the future development trends for this technology are summarized.