Computational modelling provides neuroscience with a set of powerful techniques for formulating and testing quantitative hypotheses about neural function. Our programme of work with the basal ganglia (BG) assumes that these nuclei play a central role in solving the problem of action selection: how is the competition between multiple, simultaneous requests for behavioural execution, resolved in the brain? Our work has been conducted at several levels of structural description: from conductance-based single neuron models, to high (systems) level models that represent whole populations of neurons by their mean firing rate. In (Humphries et al 2006) we described a large scale model of the basal ganglia which used spiking neurons. The overall architecture of this model was the same as that used in our previous, systems level model (Gurney et al., 2001). However, we also incorporated many additional physiologically plausible details including: effects of dopamine in the subthalamic nucleus (STN) and globus pallidus (GP), transmission delays between neurons, and specific distributions of synaptic inputs over dendrites. All main parameters were derived from experimental studies. We found that the BG circuitry supported action selection, which deteriorates under dopamine-depleted and dopamine-excessive conditions in a manner consistent with some pathologies associated with those dopamine states. Crucially, we also validated the model against data describing oscillatory properties of BG, including γ-band (30-80 Hz) oscillations (Brown et al., 2002), and dopamine-modulated slow (∼1 Hz) waves (Magill et al., 2001). From the results, we derived the following novel predictions about the STN-GP feedback loop: (1) the functional coupling in the loop is increased under dopamine depletion; (2) the loop does not show pacemaking activity under normal conditions in vivo; (3) the loop has a resonant frequency in the γ-band. More recently we have constructed an anatomically plausible model of the GABAergic components of the striatal microcircuit (Humphries et al., 2009). This circuit is formed by the dominant medium-spiny projection neurons (MSNs) and fast-spiking interneurons (FSIs). To capture the anatomy as realistically as possible, we constructed our model in three-dimensions, implementing detailed neuron-for-neuron connectivity. This effort drew on a slew of micro-anatomical data pertaining to the dendritic arborisation of MSNs and FSIs. The anatomical model was instantiated with our new dopamine-modulated neuron models of the MSNs and FSIs. The MSN model was a reduced form of a detailed compartmental model (Moyer et al., 2007) which was, in turn, constrained by a wealth of physiological data describing the effects of dopamine on voltage gated membrane currents and post-synaptic (ligand-gated) currents. A new model of gap junctions between the FSIs was introduced and tuned to experimental data. Finally, we developed a novel spike-train clustering method, suitable for large-scale models; applying this to the outputs of the model allowed us to find groups of synchronised neurons at multiple time-scales. We found that, with realistic in vivo background input, small assemblies of synchronised MSNs spontaneously appear, consistent with experimental observations (Carrillo-Reid et al 2008). The number of assemblies and the time-scale of synchronisation were strongly dependent on the simulated concentration of dopamine. Such small cell assemblies forming spontaneously only in the absence of dopamine may contribute to motor control problems seen in humans and animals following loss of dopamine cells. We dissected the contributions of the circuit elements to the formation of the cell assemblies, and found that the FSI input was crucial in desynchronising the MSN activity. We showed that feed-forward GABAergic input from the FSIs counter-intuitively increases the firing rate of the MSNs. Our models suggest that, in healthy striatum, phasic changes in FSI activity could act to locally and temporarily promote MSN responses to ongoing cortical input, performing a “selection” computation on cortical inputs without using winner-takes-all. In summary, the construction of biologically realistic models of the basal ganglia at multiple levels of structural description requires anatomical and physiological data of many forms relating to: anatomical pathways, microcircuit connectivity, details of dendritic innervation, and physiological data on ion channels. We therefore look forward to an increasing interplay between the experimental and computational neuroscience of the basal ganglia.