Japanese knotweed is an aggressive alien species in Europe, North America, and Australia, causing a range of environmental problems. Eradication of Japanese knotweed is proving to be a difficult task, because the plant is able to propagate generatively by intra- and interspecific hybridization, and vegetatively from shoot and tiny rhizome pieces. Despite the economic consequences of Japanese knotweed on natural and built environments, its physiology is not yet fully understood; especially important are sink-source relations between old and young parts of the rhizome and growth of lateral and latent rhizome buds. Current methods of chemical control include three types of phloem-mobile herbicides, such as glyphosate, imazapyr, and synthetic auxins. These herbicides have limitations on their use, and all fail to eradicate the plant completely, for the reasons discussed in this review. Our aim is to suggest prospective approaches to enable chemical eradication: use of signals to induce controlled growth and development of quiescent rhizome buds; use of phytohormones, sugars, and light to increase allocation of phloem-mobile herbicides to the rhizome; use of xylem-mobile herbicides to exterminate the old rhizome parts; and use of different phloem-mobile herbicides at different growth stages.