Synapses are crucial elements for computation and information transfer in both real and artificial neural systems. Recent experimental findings and theoretical models of pulse-based neural networks suggest that synaptic dynamics can play a crucial role for learning neural codes and encoding spatiotemporal spike patterns. Within the context of hardware implementations of pulse-based neural networks, several analog VLSI circuits modeling synaptic functionality have been proposed. We present an overview of previously proposed circuits and describe a novel analog VLSI synaptic circuit suitable for integration in large VLSI spike-based neural systems. The circuit proposed is based on a computational model that fits the real postsynaptic currents with exponentials. We present experimental data showing how the circuit exhibits realistic dynamics and show how it can be connected to additional modules for implementing a wide range of synaptic properties.