The orbitofrontal cortex receives multi-modality sensory inputs, including olfactory input, and is thought to be involved in conscious perception of the olfactory image of objects. Generation of olfactory consciousness may require neuronal circuit mechanisms for the "binding" of distributed neuronal activities, with each constituent neuron representing a specific component of an olfactory percept. The shortest neuronal pathway for odor signals to reach the orbitofrontal cortex is olfactory sensory neuron-olfactory bulb-olfactory cortex-orbitofrontal cortex, but other pathways exist, including transthalamic pathways. Here, we review studies on the structural organization and functional properties of the shortest pathway, and propose a model of neuronal circuit mechanisms underlying the temporal bindings of distributed neuronal activities in the olfactory cortex. We describe a hypothesis that suggests functional roles of gamma oscillations in the bindings. This hypothesis proposes that two types of projection neurons in the olfactory bulb, tufted cells and mitral cells, play distinct functional roles in bindings at neuronal circuits in the olfactory cortex: tufted cells provide specificity-projecting circuits which send odor information with early-onset fast gamma synchronization, while mitral cells give rise to dispersedly-projecting feed-forward binding circuits which transmit the response synchronization timing with later-onset slow gamma synchronization. This hypothesis also suggests a sequence of bindings in the olfactory cortex: a small-scale binding by the early-phase fast gamma synchrony of tufted cell inputs followed by a larger-scale binding due to the later-onset slow gamma synchrony of mitral cell inputs. We discuss that behavioral state, including wakefulness and sleep, regulates gamma oscillation couplings across the olfactory bulb, olfactory cortex, and orbitofrontal cortex.