Synaptic interactions are essential to neural network models of all levels of complexity.
In this paper, we review several types of models which address these goals. Synaptic currents are mediated by ion channels activated by neurotransmitter released from presynaptic terminals. Kinetic models are a powerful formalism for the description of channel behavior, and are therefore well-suited to the description of synaptic interactions, both traditional and neuromodulatory. Although full representation of the molecular details of the synapse generally requires highly complex kinetic models, we focus on simpler kinetic models which are very efficient to compute. We show how these models capture the time courses of several types of synaptic responses as well as the important phenomena of summation, saturation and desensitization.