Electrostatic levitation and transportation of lunar dust had been one of the most interesting and controversial problems since the Apollo era. It is not only significant clues to study the evolution of lunar surface material, but also a key factor which should be considered in lunar mission. On lunar surface, the dust grains are electrostatically charged by electron deposition, photoemission, and secondary electron emission. With the charge processes, an electrostatic field might be formed on lunar near-surface. As a result, dust grains could be lifted. However, the electrostatic levitation and transportation process of lunar dust grains are still not clear. Shortage in comprehension of electrostatic properties of lunar dust grains, simulation of electrostatic levitation and transportation, and landing detection of lunar dust environment might be the main factors which limit the further knowledge of electrostatic levitation and transportation of lunar dust grains. To satisfy the need of lunar science and future lunar missions, development of lunar dust simulant, measurement of electrostatic properties of lunar dust, simulation of electrostatic levitation and transportation, and detection of lunar dust environment are important aspects in the study of lunar dust in the future.