Decades of work in vivo and in vitro have provided a wealth of data on the properties of the reciprocal dendrodendritic synapses that connect olfactory bulb mitral and granule cells. However, hypotheses about the function of these connections have changed relatively little. These synapses are believed to mediate recurrent and lateral inhibition and thus, by analogy with lateral inhibition in other systems, have been proposed to play a role in sharpening mitral cell receptive fields and in generating oscillatory spiking in mitral cells. This description is likely to be partially accurate, but is likely to be a rather simplified and incomplete account of the function of these connections. In particular, current hypotheses about the function of dendrodendritic circuits do not account for some of the unusual features of reciprocal synapses that may allow olfactory bulb circuits to perform special functions. Here we review recent work on the physiology and function of olfactory bulb circuits and try to link the physiological properties of reciprocal synapses particular computations that the olfactory bulb may perform.