Abstract concepts are relevant to a wide range of disciplines, including cognitive science, linguistics, psychology, cognitive, social, and affective neuroscience, and philosophy. This consensus paper synthesizes the work and views of researchers in the field, discussing current perspectives on theoretical and methodological issues, and recommendations for future research. In this paper, we urge researchers to go beyond the traditional abstract-concrete dichotomy and consider the multiple dimensions that characterize concepts (e.g., sensorimotor experience, social interaction, conceptual metaphor), as well as the mediating influence of linguistic and cultural context on conceptual representations. We also promote the use of interactive methods to investigate both the comprehension and production of abstract concepts, while also focusing on individual differences in conceptual representations. Overall, we argue that abstract concepts should be studied in a more nuanced way that takes into account their complexity and diversity, which should permit us a fuller, more holistic understanding of abstract cognition.