A working hypothesis is proposed for piriform cortex (PC) and other olfactory cortical areas that redefines the traditional functional roles as follows: the olfactory bulb serves as the primary olfactory cortex by virtue of encoding 'molecular features' (structural components common to many odorant molecules) as a patchy mosaic reminiscent of the representation of simple features in primary visual cortex. The anterior olfactory cortex (that has been inappropriately termed the anterior olfactory nucleus) detects and stores correlations between olfactory features, creating representations (gestalts) for particular odorants and odorant mixtures. This function places anterior olfactory cortex at the level of secondary visual cortex. PC carries out functions that have traditionally defined association cortex--it detects and learns correlations between olfactory gestalts formed in anterior olfactory cortex and a large repertoire of behavioral, cognitive and contextual information to which it has access through reciprocal connections with prefrontal, entorhinal, perirhinal and amygdaloid areas. Using principles derived from artificial networks with biologically plausible parallel-distributed architectures and Hebbian synaptic plasticity (i.e. adjustments in synaptic strength based on locally convergent activity), functional proposals are made for PC and related cortical areas. Architectural features incorporated include extensive recurrent connectivity in anterior PC, predominantly feedforward connectivity in posterior PC and backprojections that connect distal to proximal structures in the cascade of olfactory cortical areas. Capabilities of the 'reciprocal feedforward correlation' architecture that characterizes PC and adjoining higher-order areas are discussed in some detail. The working hypothesis is preceded by a review of relevant anatomy and physiology, and a non-quantitative account of parallel-distributed principles. To increase the accessibility of findings for PC and to advertise its substantial potential as a model for experimental and modeling analysis of associative processes, parallels are described between PC and the hippocampal formation, inferotemporal visual cortex and prefrontal cortex.