The problem addressed in the paper is twofold. First, the estimation of unknown robot parameters is carried out using three different approaches, namely the gradient descent method, extended Kalman filter, and dynamic regressor extension and mixing, to evaluate their performance as applied to the two-link planar elbow robot arm. Second, an indirect adaptive inverse dynamics controller based on the obtained estimates is designed to study performance achieved by the estimation methods in the control problem. The obtained results show advantages of the dynamic regressor extension and mixing in the both addressed problems.