Synchronized bursts (SBs) with complex structures are common in neuronal cultures. Although the phenomenon of SBs has been discovered for a long time, its origin is still unclear. Here, we investigate the properties of these SBs in cultures grown on a multi-electrode array. We find that structures of these SBs are related to the different developmental stages of the cultures and these structures can be modified by changing the magnesium concentration in the culture medium; indicating that synaptic mechanism is involved in the generation of SBs. A model based on short term synaptic plasticity (STSP), recurrent connections and astrocytic recycling of neurotransmitters has been developed successfully to understand the observed structures of SBs in experiments. A phase diagram obtained from this model shows that networks exhibiting SBs are in a complex oscillatory state due to large enough positive feedback provided by synaptic facilitation and recurrent connections. In this model, while STSP controls the fast oscillations (∼ 100 ms) within a SB, the astrocytic recycling determines the slow time scale (∼10 s) of inter-burst intervals. Our study suggests that glia-neuron interactions can be important in the understanding of the complex dynamics of neuronal networks.