The chapter considers the motivation for Alexander the Great’s expedition to India, which took him beyond the limits of the Persian Empire he had set out to conquer. Ambition (pothos) is seen as more probable than either strategic necessity or scientific curiosity. The course of the campaign from November 326 to July 325 BC is outlined, and the reasons for the savagery of the fighting during the journey down the Indus are considered. The chapter also reviews the impact of Alexander’s encounter with the ‘naked philosophers’ of Taxila. One of them, Calanus, travelled with Alexander until his death, and it is suggested that his conversation made an impression on another of Alexander’s companions, the philosopher Pyrrho, who became known as the founder of scepticism. The paper also reviews the legacy of Alexander in India. Foremost is the detailed account of India written by Megasthenes, a former member of Alexander’s army and ambassador from Seleucus to Candragupta. Indo-Greek dynasties persisted in north-west India for two centuries after Alexander’s death, but to narrate this history would go beyond the subject. The chapter looks briefly at the evidence for other Greeks who left records of their residence in India.