Compared to solar radio bursts, interplanetary (IP) radio bursts with lower radiation frequencies are generally believed to originate in the interplanetary space far from the low corona. The cutoff by Earth's ionosphere makes the ground-based observations for it impossible. Parker Solar Probe (PSP), launched by the National Aeronautics and Space Administration (NASA) to explore the Sun with the closer heliocentric distance than any previous spacecraft, provides an opportunity to study the low-frequency radio burst. The radio spectrometer it carries can observe radio radiation in the frequency range of 10 kHz--19.17 MHz. PSP can approach the radiation source region of the IP type III radio burst. Therefore, it has an unprecedented advantage to observe the interplanetary radio bursts. This paper reviews the studies about type III radio bursts observed by PSP so far. These studies include the occurrence rate, polarization, scattering, cutoff frequency, possible radiation mechanisms, and related radiation source regions of radio bursts and so on. Finally, future research prospects are discussed.