Mindfulness, whether distinguished as a state, trait, or training, is central to a growing wave of interest in meditation. Theoretical development has been called for in order to clarify confusion about mindfulness from a scientific perspective. Ideally, such development will allow ingress for more traditional perspectives and guide inclusive research on the wider range of meditation practices. To address this call, we outline a new approach for understanding mindfulness and related meditative experience that accommodates diverse perspectives. In accord with other integrative approaches, we employ foundational psychological constructs (namely, attention, intention, and awareness) to understand mindfulness. In contrast to other theoretical perspectives, however, we utilize this foundation to derive novel psychological constructs needed to better explain mindfulness and important features of meditative experience more widely. The contemplative cognition framework integrates three attention-related processes entailed by a variety of contemplative practices: intended attention, attention to intention, and awareness of transient information. After delineating this set of three processes, we explain how they can cooperate to promote a contemplative range of metacognition about attention, intention, and awareness, as well as enhanced regulation of cognition, emotion, and behavior. The contemplative cognition framework (a) overcomes discrepancies in mindfulness research; (b) accounts for contextual and motivational aspects of training; (c) supports investigation from phenomenological, information processing, neurophysiological, and clinical perspectives; and (d) enables investigations on various contemplative states, traits, and practices to inform one another. This new approach has potential for advancing a more inclusive, productive, and theory-driven science of mindfulness and meditation.