This chapter investigates why Pāṇini has been called the world’s first computational linguist and situates Pāṇinian grammar within the context of formal language theory and issues of generative capacity, which have been of huge importance in the development of modern linguistic theory since Chomsky's earliest work. Existing claims regarding the generative capacity of Pāṇini’s system are shown to be inadequate, and a new assessment of the power of the Aṣṭādhyāyī is provided.