MOST excitatory synaptic connections occur on dendritic spines¹. Calcium imaging experiments have suggested that spines constitute individual calcium compartments^2,3, but recent results have challenged this idea^4,5. Using two-photon microscopy⁶ to image fluorescence with high resolution in strongly scattering tissue, we measured calcium dynamics in spines from CA1 pyramidal neurons in slices of rat hippocampus. Subthreshold synaptic stimulation and spontaneous synaptic events produced calcium accumulations that were localized to isolated spines, showed stochastic failure, and were abolished by postsynaptic blockers. Single somatic spikes induced fast-peaking calcium accumulation in spines throughout the cell. Pairing of spikes with synaptic stimulation was frequently cooperative, that is, it resulted in supralinear calcium accumulations. We conclude: (1) calcium channels exist in spine heads; (2) action potentials invade the spines; (3) spines are individual calcium compartments; and (4) spines can individually detect the temporal coincidence of pre- and postsynaptic activity, and thus serve as basic functional units of neuronal integration.