Electrons have so little mass that in less than a second they can tunnel through potential energy barriers that are several electron-volts high and several nanometers wide. Electron tunneling is a critical functional element in a broad spectrum of applications, ranging from semiconductor diodes to the photosynthetic and respiratory charge transport chains. Prior to the 1970s, chemists generally believed that reactants had to collide in order to effect a transformation. Experimental demonstrations that electrons can transfer between reactants separated by several nanometers led to a revision of the chemical reaction paradigm. Experimental investigations of electron exchange between redox partners separated by molecular bridges have elucidated many fundamental properties of these reactions, particularly the variation of rate constants with distance. Theoretical work has provided critical insights into the superexchange mechanism of electronic coupling between distant redox centers. Kinetics measurements have shown that electrons can tunnel about 2.5 nm through proteins on biologically relevant time scales. Longer-distance biological charge flow requires multiple electron tunneling steps through chains of redox cofactors. The range of phenomena that depends on long-range electron tunneling continues to expand, providing new challenges for both theory and experiment.