Long-distance dispersal (LDD) of plants poses challenges to research because it involves rare events driven by complex and highly stochastic processes. The current surge of renewed interest in LDD, motivated by growing recognition of its critical importance for natural populations and communities and for humanity, promises an improved, quantitatively derived understanding of LDD. To gain deep insights into the patterns, mechanisms, causes, and consequences of LDD, we must look beyond the standard dispersal vectors and the mean trend of the distribution of dispersal distances. “Nonstandard” mechanisms such as extreme climatic events and generalized LDD vectors seem to hold the greatest explanatory power for the drastic deviations from the mean trend, deviations that make the nearly impossible LDD a reality.