Recent experimental evidence suggests that glial cells are more than just supporting cells to neurons — they play an active role in signal transmission in the brain. We herein propose to investigate the importance of these mechanisms and model neuron-glia interactions at synapses using three approaches: A parametric model that takes into account the underlying mechanisms of the physiological system, a non-parametric model that extracts its input-output properties, and an ultra-low power, fast processing, neuromorphic hardware model. We use the EONS (Elementary Objects of the Nervous System) platform, a highly elaborate synaptic modeling platform to investigate the influence of astrocytic glutamate transporters on postsynaptic responses in the detailed micro-environment of a tri-partite synapse. The simulation results obtained using EONS are then used to build a non-parametric model that captures the essential features of glutamate dynamics. The structure of the non-parametric model we use is specifically designed for efficient hardware implementation using ultra-low power subthreshold CMOS building blocks. The utilization of the approach described allows us to build large-scale models of neuron/glial interaction and consequently provide useful insights on glial modulation during normal and pathological neural function.