In this paper, synchronization for uncertain fractional order chaotic systems is investigated. By using the fractional order extension of the Lyapunov stability criterion, a linear feedback controller and an adaptive controller are designed for synchronizing uncertain fractional order chaotic systems without and with unknown external disturbance, respectively. Quadratic Lyapunov functions are used in the stability analysis of fractional-order systems, and fractional order adaptation law is constructed to update design parameter. The proposed methods can guarantee that the synchronization error converges to zero asymptotically. Finally, illustrative examples are given to confirm the theoretical results.