This article begins with a brief introductory account of the vicissitudes of the academic studies on extraordinary capacities. Thereafter, the stereotyped passages in which iddhi and abhiññā occur as a meditative attainment achieved within a Buddhist path of liberation are presented and the interpretation of these two terms is discussed. After these preparatory opening remarks, the Vedic background of iddhi and abhiññā is treated with regards to three aspects. First, the speculative idea sustained by some scholars that would see the body made of mind (manomaya-kāya) as the base and tool to perform iddhis and abhiññās is discussed on the basis of the Vedic evidence. Secondly, the term ‘divine’ (dibba) which occurs in the description of some abhiññās is compared with the use of the corresponding Vedic terms and with the Vedic idea of a divine power behind the functioning of the faculties. Finally, the abhiññā called ‘the knowledge of degeneration and ascent of beings’ (cutūpapātañāṇa) is compared with a couple of narratives involving the oneiric state within the Upaniṣads, showing some similarities between the two accounts.