This review is based on many publications from the US and some from the former Soviet Union. It briefly describes the sources of lunar dust. The problems posed to the past Apollo missions are summarized. The physical properties of lunar soils, such as cohesion, angle of repose, angle of friction, and bearing capacity, as reported by scientists from these two nations, are compared. The composition of lunar soils is described in terms of acidic and basic components. Since lunar soils are mainly silicates, we are the first to point out the importance of the Lewis acid-base interaction to the cohesion and adhesion of lunar dust. The adhesion of lunar dust is similar to that of a xerographic developer. For the adhesion between lunar dust and dissimilar materials, both van der Waals and electrostatic interactions can be the driving force, depending on the size of the dust particles. For particles smaller than 50 mu m, van der Waals interaction predominates, while for those larger than 50 mu m, electrostatic interaction controls. For the electrostatic interaction, lunar dust should charge positively. If lunar dust is pre-charged, e.g, by solar wind, the electrostatic interaction should predominate regardless of the size of the particles. It is important to note that for the electrostatic interaction, both electronic and ionic mechanisms can influence charge exchange. Thus, the Lewis type acid-base interaction can also affect the charge exchange. Experimental work with a simulated lunar dust is recommended for the elucidation of the adhesion and cohesion mechanisms. Before that, all methods of control of lunar dust are, at best, speculative.