The relationship between structure, dynamics, and function of neural networks in nervous systems is still an open question in the neuroscience community. Nevertheless, for certain areas of the mammalian nervous system we do have sufficient data to impose constraints on the organisation of the network structure. One of these areas is the medial entorhinal cortex which contains cells with hexagonally repeating spatial receptive fields, called grid cells. Another intriguing property of entorhinal cortex and other cortical regions is a population oscillatory activity, with frequency in the theta (4-10 Hz) and gamma (30-100 Hz) range. This leads to a question, whether these oscillations are a common circuit mechanism that is functionally relevant and how the oscillatory activity interacts with the computation performed by grid cells. This thesis deals with applying the continuous attractor network theory to modelling of the microcircuit of layer II in the medial entorhinal cortex. Based on recent experimental evidence on connectivity between stellate cells, and fast spiking interneurons, I first develop a two-population spiking attractor network model that is capable of reproducing the activity of a population of grid cells in layer II. The network was implemented with exponential integrate and fire neurons that allowed me to address both the attractor states and the oscillatory activity in this region. Subsequently, I show that the network can produce theta-nested gamma oscillations with properties that are similar to the cross-frequency coupling observed in vivo and in vitro in entorhinal cortex, and that these theta-nested gamma oscillations can co-exist with grid-like receptive fields generated by the network. I also show that the connectivity inspired by anatomical evidence produces a number of directly testable predictions about the firing fields of interneurons in layer II of the medial entorhinal cortex. The excitatory-inhibitory attractor network, together with the theta-nested gamma oscillations, allowed me to explore potential relationships between nested gamma oscillations and grid field computations. I show, by varying the overall level of excitatory and inhibitory synaptic strengths, and levels of noise, in the network, that this relationship is complex, and not easily predictable. Specifically, I show that noise promotes generation of grid firing fields and theta-nested gamma oscillations by the model. I subsequently demonstrate that theta-nested gamma oscillations are dissociable from the grid field computations performed by the network. By changing the relative strengths of interactions between excitatory and inhibitory neurons in the network, the power and frequency of the gamma oscillations changes without disrupting the rate-coded grid field computations. Since grid cells have been suggested to be a part of the spatial cognitive circuit in the brain, these results have potential implications for several cognitive disorders, including autism and schizophrenia, as well as theories that propose a cognitive role for gamma oscillations.