Long-term modification of synaptic strength is one of the basic mechanisms of memory formation and activity-dependent refinement of neural circuits. This idea was purposed by Hebb to provide a basis for the formation of a cell assembly. Repetitive correlated activity of pre-synaptic and post-synaptic neurons can induce long-lasting synaptic strength modification, the direction and extent of which depends critically on the temporal order of pre-synaptic and postsynaptic activity. This process, “spike timing dependent plasticity” (STDP), is well suited for creating neural networks with predictive behavior. The cellular mechanisms of STDP are not well understood. But it is believed that a transient increase in postsynaptic intracellular calcium plays a central role and downstream to calcium, several protein kinases and phosphatases signal for the changes in synapse. In most cases, induction of LTD and LTP depends on activation of NMDA receptors that seems to act as coincidence detector by the virtue of their particular property that channel opens only when glutamate binds to its receptor and magnesium block is removed by coincidence depolarization. The degree of channel opening will then determine the amount of calcium passing through the pore. At first look it seems that high levels of calcium induce LTP and moderate calcium levels favor LTD. If this was the case, we were to observe an additional LTD window in positive spike timing range. However, such an additional LTD was not observed in most studies that have mapped out the asymmetric spike timing window. It seems that other spatial and temporal patterns of calcium transient are also important in synaptic modification. Another interesting feature of STDP is its effect on the behavior of neural networks. According to modeling studies, STDP causes a balanced irregular firing regime in networks of neurons sensitive to the pre-synaptic action potentials. Molecular biology and computational tools are now beginning to interpret synaptic plasticity in terms of quantitative and spatiotemporal rules, which are likely to bridge the gap between synaptic physiology and neural network behavior. This review will try to represent a perspective of the latest findings in this field and current opinion and possible future vista.