We demonstrate that spiking neural networks encoding information in the timing of single spikes are capable of computing and learning clusters from realistic data. We show how a spiking neural network based on spike-time coding and Hebbian learning can successfully perform unsupervised clustering on real-world data, and we demonstrate how temporal synchrony in a multi-layer network can induce hierarchical clustering. We develop a temporal encoding of continuously valued data to obtain adjustable clustering capacity and precision with an e#cient use of neurons: input variables are encoded in a population code by neurons with graded and overlapping sensitivity profiles. We also discuss methods for enhancing scale-sensitivity of the network and show how the induced synchronization of neurons within early RBF layers allows for the subsequent detection of complex clusters.