Recent expositions by Dan Zahavi, Thomas Metzinger, Galen Strawson and others have foregrounded questions about the nature and existence of self in phenomenological and cognitive terms, while also recognising that Buddhism and other Asian traditions had tackled these questions in the past. A key aspect of any inter-cultural discussion is the clarification of terms. Looking at Hindu-Buddhist debates about ātman (usually translated as ‘self’) and related concepts about ‘I’ and ‘person’, I offer suggestions for how understanding different senses of self in these classical debates also help engage with contemporary Western discussions over whether there is a self or not.