Recent progress towards a complete understanding of the AdS/CFT correspondence has been illuminated by the appearance of integrable structures on both sides of the duality. On the gauge theory, integrability has been found beyond one loop in some restricted sectors, which has lead to the suggestion of a long-range Bethe ansatz. The quantum Bethe ansatz on the string theory side has a remarkably similar structure to the gauge theory ansatz. We will discuss these and related developments, and present a general expression for the first quantum correction to the string Bethe ansatz.