How the olfactory bulb organizes and processes odor inputs through fundamental operations of its microcircuits is largely unknown. To gain new insight we focus on odor-activated synaptic clusters related to individual glomeruli, which we call glomerular units. Using a 3D model of mitral and granule cell interactions supported by experimental findings, combined with a matrix-based representation of glomerular operations, we identify the mechanisms for forming one or more glomerular units in response to a given odor, how and to what extent the glomerular units interfere or interact with each other during learning, their computational role within the olfactory bulb microcircuit, and how their actions can be formalized into a theoretical framework in which the olfactory bulb can be considered to contain "odor operators" unique to each individual. The results provide new and specific theoretical and experimentally testable predictions. T he organization of olfactory bulb network elements and their synaptic connectivity has evolved to subserve special computational functions needed for odor detection and recognition (1-5). Key to this organization are the olfactory glomeruli, collecting input from olfactory receptor neuron subsets. These connect to the dendrites of mitral, tufted, and periglomerular cells, and the mitral and tufted cells in turn connect to granule cells. We term these interconnected cells a cluster, and a cluster related to a given glomerulus is a glomerular unit (GU), often visualized as a column of granule cell bodies located below a glomerulus (6, 7). The existence of such GUs has also been suggested from 2-deoxyglucose (8) and voltage-sensitive dye studies (9).Understanding the neural basis of odor processing therefore requires understanding the computational functions and role of GUs. These issues, which are difficult or impossible in experiments, can be conveniently explored using realistic computational models, provided they are able to explain and reproduce crucial experimental findings on glomerular clusters or units.Analyzing synaptic interactions between cells with overlapping dendrites requires modeling in real 3D space. Scaling up to the network level further requires scaling up realistic structural and functional properties to many thousands of cells (10). Building on this unique approach, we show that this model generates columnar clusters of cells related to individual glomeruli, as in the experiments, and further demonstrates mechanisms of odor processing within and between the GUs. Finally, interpreting this network activity requires a theoretical framework, incorporating distributed activated glomeruli within the global network, for which we introduce the concept of the odor operator. The results provide a basis for extension to the glomerular level on the one hand and interactions with olfactory cortex on the other.