The radio emission mechanisms, especially the coherent radio emission mechanisms of radio bursts, are one of the most complicated and controversial topics in astrophysics. Due to the complex influence of multiple physical factors, theoretical studies of coherent radio emission mechanisms are very difficult. There has been a constant controversy between the two types of coherent emission mechanisms, i.e., the plasma emission and the electron cyclotron maser emission, for a long time. In recent years, people have been trying to apply the fully-kinetic Particle-in-Cell (PIC) numerical simulations to the study of coherent radio emissions, and have made some positive progress. In addition to reviewing some existing problems and difficulties in this topic, this paper will focus on the research of PIC simulations for the coherent radio emissions from space plasmas and the main progress in recent years.