The 'Aryan invasion' debate revolves around the origins and migration of the Indo-Aryan people into the Indian subcontinent and their relationship with the indigenous populations, particularly the Harappan (Indus Valley) Civilization.

The Aryan Invasion Theory (AIT), prevalent for much of the 19th and 20th centuries, posited that a group of nomadic, horse-riding people, termed 'Aryans,' invaded India from Central Asia around 1500 BCE. They were believed to have conquered the indigenous Dravidian-speaking Harappans, leading to the decline of the Indus Valley Civilization and the establishment of Vedic culture. Evidence cited included linguistic similarities between Sanskrit and European languages (Indo-European family), the presence of horses and chariots in Vedic texts, and descriptions of conflicts in the Rigveda.

However, the AIT has faced significant challenges and evolved into the Aryan Migration Theory (AMT), which suggests a more gradual process of migration and cultural diffusion rather than a violent invasion. Critics of the AIT point to a lack of clear archaeological evidence for a large-scale invasion, such as widespread destruction or distinct 'Aryan' material culture. Genetic studies have also provided complex and often contradictory evidence regarding population movements.

An alternative, the Out of India Theory (OIT), proposes that the Indo-Aryans were indigenous to India and migrated outwards to other parts of the world. This theory, however, lacks widespread academic consensus.

The debate remains complex and multidisciplinary, involving linguistics, archaeology, genetics, and textual analysis. While the idea of a destructive 'invasion' has largely been discarded, the nature, timing, and impact of Indo-Aryan migrations and their interaction with existing cultures continue to be subjects of intense academic discussion and research.