In insulating liquid, a conductive particle becomes charged through the interaction with a conductor exposed to an applied field. Then, it migrates in the action of both electric field and fluid and causes the enhancement of local field when it is in proximity of the conductor with opposite polarity. The enhancement will lead to partial discharge (PD) and may even ignite full gap breakdown in special cases. This study reviews comprehensive researches relevant to these topics. In the first place, several theoretical methods about how to obtain the charges held by a conductive particle with known potential are introduced, so are experimental methods. Then, forces acting on the charged particle in liquid are classified, and its migration characteristics, as well as influential factors, are described. Subsequently, PD and breakdown mechanisms of liquid initiated by conductive particles are presented. The latter involves two cases: electric-field enhancement when the particle concentration is low and bridging phenomenon when it is high. At last, two important, but frequently ignored factors, i.e. dielectric barrier and oil flow, are highlighted, and the authors' suggestions for future work are put forward.