Elastic and inelastic scattering, one-nucleon transfers [mostly (8Li, Li7)] and the (8Li,α) fusion-evaporation reaction have been studied on a variety of targets (A=1–58) at E(8Li)≊13–20 MeV using the University of Michigan–University of Notre Dame radioactive nuclear beam (RNB) facility. The latter, which produces an energy-resolved (∼500 keV FWHM), focused beam with intensity ≳106 Li8/s, permitted measurements to selected nuclear levels with cross sections down to approximately 1 mb/sr. Based on the systematics of the measured Li8 elastic scattering an appropriate Li8 optical potential was deduced. Large inelastic scattering cross sections (and B[E2↑]) are observed for →88Li0.98*. Large cross sections are also observed for the (8Li,7Li) transfer reaction corresponding to quasielastic (viz., Q≊0) neutron transfer to selected high spin excited levels in the residual nucleus. The (8Li,α) fusion-evaporation reaction also appears to be significant and can produce very-high-energy α particles, viz., Eα≫Ebeam. Although observed using Li8, these features appear to be important for many RNB-induced reactions and they must be considered, for example, in nucleosyntheis calculations involving Li8 and other short-lived radioactive nuclei.