Astrocytes were classically considered as simple supportive cells for neurons without a significant role in information processing by the nervous system. However, considerable amounts of evidence obtained by several groups during the past years demonstrated the existence of a bidirectional communication between astrocytes and neurons, which prompted a re-examination of the role of astrocytes in the physiology of the nervous system. While neurons base their excitability on electrical signals generated across the membrane, astrocytes base their cellular excitability on variations of the Ca2+ concentration in the cytosol. This article discusses our current knowledge of the properties of the synaptically evoked astrocyte Ca2+ signal, which reveals that astrocytes display integrative properties for synaptic information processing. Astrocytes respond selectively to different axon pathways, discriminate between the activity of different synapses and their Ca2+ signal is non-linearly modulated by the simultaneous activity of different synaptic inputs. Furthermore, this Ca2+ signal modulation depends on astrocyte cellular intrinsic properties and is bidirectionally regulated by the level of synaptic activity. Finally, astrocyte Ca2+ elevations can trigger the release of gliotransmitters, which modulate neuronal activity as well as synaptic transmission and plasticity, hence granting the bidirectional communication with neurons. Consequently, astrocytes can be considered as cellular elements involved in information processing by the nervous system.