This chapter outlines current interpretation of computational aspects of GABAergic circuits of the striatum. Recent hypotheses and controversial matters are reviewed. Quantitative aspects of striatal synaptology relevant to computational models are considered, with estimates of the connectivity of the spiny projection neurons and fast-spiking interneurons. Against this background, insights into the computational properties of inhibitory circuits based on analysis and simulation of simple models are discussed. The paper concludes with suggestions for further theoretical and experimental studies.