The ability to understand and use language referring to abstract entities, events, and qualities (e.g., contempt, respect, kindness) is arguably a uniquely human faculty. The objective is to deepen our understanding of the acquisition and representation in the mind/brain of abstract concepts. We adopt: (1) a cross-linguistic perspective, motivated by the existence of culturally-bounded abstract concepts, expressed in languages with words that cannot be easily translated; (2) an interdisciplinary perspective, motivated by our aim to explore systematically the developmental, cognitive, computational and neural aspects of abstract knowledge. We contrast two explicit working hypotheses: the Embodiment Hypothesis (EH) and the Abstraction from Language Hypothesis (ALH). According to the former, abstract knowledge originates in “conceptual metaphors”: the use of a concrete conceptual domain of knowledge to describe an abstract conceptual domain. The latter proposes that abstract concepts are learned by way of the statistical properties of language, since words that behave similarly within a language (in terms of statistical co-occurrence) are also often conceptually related. These two hypotheses are associated with largely different predictions: according to ALH (but not EH) language development is a phylogenetic and ontogenetic prerequisite to the development of abstract concepts. Regarding neural implementation, a close connection of abstract concepts with sensorimotor representations is predicted by EH, while ALH is compatible with a main involvement of the left hemispheric classical language areas. We develop these hypotheses using tools from linguistics and computational modelling. We test predictions in (1) behavioural studies; (2) developmental studies of typically developing and cognitively impaired children and (3) cognitive neuroscience (in ERP, fMRI, TMS and patients’ studies.