The piriform cortex (PCx) receives direct input from the olfactory bulb (OB) and is the brain's main station for odor recognition and memory. The transformation of the odor code from OB to PCx is profound: mitral and tufted cells in olfactory glomeruli respond to individual odorant molecules, whereas pyramidal neurons (PNs) in the PCx responds to multiple, apparently random combinations of activated glomeruli. How these “discontinuous” receptive fields are formed from OB inputs remains unknown. To study these questions, we used brain slices of PCx combined with electrophysiology, calcium imaging, optogenetics, uncaging and modeling. We found that counter to the prevailing view that olfactory PNs sum their inputs passively, NMDA spikes within individual dendrites can both amplify OB inputs and impose combination selectivity upon them, while their ability to compartmentalize voltage signals allows different dendrites to represent different odorant combinations. Moreover, we find that these NMDA spikes can serve as a strong and robust postsynaptic signal for long term potentiation of LOT inputs into distal apical dendrites of PCx PNs. We conclude that dendrites of PCx PNs provide the nonlinear integrative and plasticity mechanisms necessary for odor learning and representation.