The discovery of dendritic spines in the late nineteenth century has prompted nearly 90 years of speculation about their physiological importance. Early observations that bulbous spine heads had very close approximations with the axon terminals of other neurons, confirmed later by ultrastructural study, led to ideas that spines enhance dendritic surface areas for making synaptic contacts. More recent application of cable and core-conductor theory to the anatomical study of spines has raised a number of new ideas about spine function. One important issue was derived from the theoretical treatment of spines as tiny dendrites with much higher input resistances than those of the larger parent dendrites. The high spine-stem resistance results in relative electrical isolation of the spine head; this causes large local depolarizations in the spine head. Several theoretical studies have also shown that if the spine-head input resistances are substantially higher than those of the parent dendrites, spines have the potential for modulating a host of biochemical and biophysical processes that might regulate synaptic efficacy. Empirical studies have documented that spine heads increase rapidly in size after afferent projections have been stimulated electrically and after animals have engaged in a single bout of ecologically important behavioral activity. Such spine head enlargement dilates the portion of the spine stem adjacent to the spine head and this process shortens the spine stem without appreciably altering overall spine length. Theoretical study shows that spine-stem shortening lowers the spine-head input resistance relative to the branch input resistance. This reduction in input resistance can enhance the transfer of electrical charge from the spine head to the parent dendrite, especially when the synaptic conductance is large relative to the spine-head input conductance. Spine-stem shortening also lowers the peak transient membrane potential in the spine head and this factor could delimit Ca2+ influx into the spine head via voltage-dependent Ca2+ channels. The modulation of Ca2+ influx by spine-stem shortening has the potential for regulating Ca2+-sensitive enzymatic activity in the spine head that could affect phosphorylation of cytoskeletal proteins maintaining spine shape and phosphorylation of proteins in the postsynaptic density. Finally, theoretical findings are described that examine the effects of voltage-dependent inward-current channels in the spine head and their ability to amplify the charge transfer due to transmitter-dependent synaptic conductances.