What is the functional significance of generating a burst of spikes, as opposed to a single spike? A dominant point of view is that bursts are needed to increase the reliability of communication between neurons. Here, we discuss the alternative, but complementary, hypothesis: bursts with specific resonant interspike frequencies are more likely to cause a postsynaptic cell to fire than are bursts with higher or lower frequencies. Such a frequency preference might occur at the level of individual synapses because of the interplay between short-term synaptic depression and facilitation, or at the postsynaptic cell level because of subthreshold membrane potential oscillations and resonance. As a result, the same burst could resonate for some synapses or cells and not resonate for others, depending on their natural resonance frequencies. This observation suggests that, in addition to increasing reliability of synaptic transmission, bursts of action potentials might provide effective mechanisms for selective communication between neurons.