Decades of research on understanding the mechanisms of attentional selection have focused on identifying the units (representations) on which attention operates in order to guide prioritized sensory processing. These attentional units fit neatly to accommodate our understanding of how attention is allocated in a top-down, bottom-up, or historical fashion. In this talk, I will focus on attentional phenomena that are not easily accommodated within current theories of attentional selection – the “attentional platypuses,” as they allude to an observation that within biological taxonomies the platypus does not fit into either mammal or bird categories. Similarly, attentional phenomena that do not fit neatly within current attentional models suggest that current models need to be revised. I list a few instances of the ‘attentional platypuses” and then offer a new approach, the Dynamically Weighted Prioritization, stipulating that multiple factors impinge onto the attentional priority map, each with a corresponding weight. The interaction between factors and their corresponding weights determines the current state of the priority map which subsequently constrains/guides attention allocation. I propose that this new approach should be considered as a supplement to existing models of attention, especially those that emphasize categorical organizations.