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Recent progress in the study of motions and reactions of single adsorbed molecules on metal surfaces induced by inelastic tunneling electrons with a scanning tunneling microscope (STM) is given an overview, with the focus on our current theoretical understanding of the elementary processes behind these phenomena. The selected topics include rotation and dissociation of O2 on Pt(111), rotation of a C2H(D)2 on Cu(100), lateral hopping of CO on Pd(110), lateral translation and desorption of NH3 on Cu(100), and controlled manipulation of chemical transformation as well as bimolecular reaction of coadsorbed species on metal surfaces. Brief descriptions are presented of how an adsorbate to overcome the potential barrier for motion and reaction by incoherent stepwise and coherent single multistep climbing of the vibrational ladders in the potential well along the reaction coordinate, and indirect excitation of the reaction coordinate mode via anharmonic coupling to the vibrational mode excited by tunneling current. Elementary processes of the mode-selective control of different motions are also discussed in conjunction with a recent experimental result of lateral hopping and desorption of a single NH3 molecule on Cu(100). Although still at a premature stage, these novel phenomena open a new world of "nano-surface-science," in which the manipulation and reaction of single adsorbates, and synthesis of a new molecular system are realized by a selective excitation of the relevant vibrational mode by tunneling electrons with an STM.