Olfaction is a fascinating sensory modality, for it deals with complex stimuli (usually complex mixtures of chemical analytes) and generates singular percepts (coffee, jasmin, bread etc), that remain stable over wide ranges of intensities, noise and input composition. Furthermore, olfactory systems accomplish these pattern recognition feats in only very few layers of processing. I will summarize experimental results on computation in a small olfactory system, focusing on the representation of such stimuli, on circuit dynamics, synchronization, learning rules and mechanisms of homeostatic regulation of activity.