Nerve signals in the form of action potentials are relayed between neurons through specialized connections called synapses via neurotransmitter released from synaptic vesicles. The release process is Ca2+ dependent, and relies on fusion of neurotransmitter filled synaptic vesicle with the presynaptic membrane. During high frequency stimulation, the amount of vesicle release increases at some synapses (e.g., frog neuromuscular junction (NMJ)), a process known as short-term plasticity. Due to the micron scale size of the presynaptic active zone where vesicle fusion takes place, experimentally study is often difficult. Thus, computational modeling can provide important insight into the mechanism of synaptic vesicle release at active zones. In the first part of my thesis, I used the frog NMJ as a model synapse for computer simulation studies aimed as testing various mechanistic hypotheses proposed to underlie short-term plasticity. Building off a recently reported excess-bindingsite model of synaptic vesicle release at the frog NMJ (Dittrich et al., 2013), I have investigated several mechanisms of short-term facilitation at the frog NMJ. My studies placed constraints on previously proposed mechanistic models, and concluded that the presence of a second calcium sensor protein on synaptic vesicles distinct from synaptotagmin, can explain known properties of facilitation observed at the frog NMJ. In addition, I was able to identify a second facilitation mechanism, which relied on the persistent binding of calcium bound synaptotagmin molecules to lipids of the presynaptic membrane. In the second part of my thesis, I investigated the structure function relationship at active zones, with the hypothesis that active zones are organized from the same basic synaptic building block consisting of a docked vesicle and a small number of closely associated voltage-gated-calcium-channels (VGCCs). To test this hypothesis, I constructed a vesicle release model of the mouse NMJ by reassembling frog NMJ model building blocks based on electron-microscopy imaging data. These two models successfully predicted the functional divergence between frog and mouse NMJ in terms of average vesicle release and short-term plasticity. In the meanwhile, I found that frog NMJ loses facilitation when VGCCs were systematically removed from active zone. By tracking Ca2+ ions from each individual VGCCs, I further show how the difference in short-term plasticity between frog and mouse NMJ may rise from their distinct release building block assemblies. In summary, I have developed a stochastic computer model of synaptic transmission, which not only shed light on the underlying mechanisms of short-term plasticity, but was also proved powerful in understanding structural and functional relationships at synaptic active zones.