The advent of high-quality 3D reconstructions of neuronal arbors has revived the hope of inferring synaptic connectivity from the geometric shapes of axons and dendrites, or 'neurogeometry'. A quantitative description of connectivity must be built on a sound theoretical framework. Here, we review recent developments in neurogeometry that can provide such a framework. We base the geometric description of connectivity on the concept of a 'potential synapse'--the close apposition between axons and dendrites necessary to form an actual synapse. In addition to describing potential synaptic connectivity in neuronal circuits, neurogeometry provides insight into basic features of functional connectivity, such as specificity and plasticity.