The 'local circuits' of the mammalian neocortex are defined within cortical columns less than 1mm across. There is mounting evidence that these fine-scale neural networks are an important organisational and functional unit. However, detailed study of the local circuitry is hampered by considerable technical difficulties; computer-based modelling therefore offers an important approach to understanding their basic properties. In this thesis, computer simulations are used to examine some of the fundamental questions associated with this class of neural network. We describe a spiking-network model which is inspired by anatomical and physiological study of local neocortical circuitry. Small, heterogeneous circuits are constructed from regular firing, rhythmic bursting and fast spiking neurons. These cells interact strongly through dynamic connections; synapses exhibit facilitation, depression, or a hybrid form of non-associative plasticity. A fast, asymmetric Hebbian process is also examined as a model of the 'Malsburg synapse', and is implemented in parallel with the non-associative fonns of plasticity. Exploration proceeds in three stages using a bottom-up methodology. First, we investigate the dynamical repertoire of the individual classes of circuit; the significance of architectural variation between circuits is addressed, and we examine the influence of fast adaptive processes in shaping network dynamics. Guided by available experimental data, circuits are connected in the second stage to create larger architectures; these are used to study interactions between the circuits. In the third stage, the inhibitory circuits implement surround and feedback inhibition, and local circuit effects of these two contrasting models are explored. Simulation results offer novel links between disparate experimental data. They also indicate how variation in the architecture of particular local circuits, and the different classes of connection between these circuits, might have functional pertinence. More generally, our findings suggest how this style of network may support a highly flexible, dynamically configurable computational architecture.