A growing body of evidence has demonstrated that multiple sources of salience tune attentional sets toward aspects of the environment, including affectively and motivationally significant categories of stimuli such as angry faces and reward-associated target locations. Recent evidence further indicates that objects that have gained personal significance through ownership can elicit similar attentional prioritization. Here we discuss current research on sources of attentional prioritization that shape our awareness of the visual world from moment to moment and the underlying neural systems and contextualize what is known about attentional prioritization of our possessions within that research. We review behavioral and neuroimaging research on the influence of self-relevance and ownership on cognition and discuss challenges to this literature stemming from different modes of conceptualizing and operationalizing the self. We argue that ownership taps into both “self-as-object,” which characterizes the self as an object with a constellation of traits and attributes, and “self-as-subject,” which characterizes the self as an agentic perceiver and knower. Despite an abundance of research probing neural and behavioral indices of self-as-object and its effects on attention, there exists a paucity of research on the influence of self-relevance of attention when self is operationalized from the perspective of a first-person subject. To begin to address this gap, we propose the Self as Ownership in Attentional Prioritization (SOAP) framework to explain how ownership increases salience through attention to external representations of self-identity (i.e., self as object) and attention to contextually mediated permission to act (i.e., self as subject).