In this chapter, the basic assumption that a robot manipulator is driven by actuators through rigid transmissions is removed, and the consequences on dynamic modeling, inverse dynamics, and feedback control problems are analyzed. Motivations for considering mechanical flexibility concentrated at the joints are discussed.Manipulatorwith elastic joints For robots with elastic joints, the dynamic model is derived with the Euler–Lagrange approach, doubling the number of generalized coordinates to account for the different relative positions of driving motors and driven links. Extensions of the model are briefly discussed, by relaxing standard simplifying assumptions (complete model) or considering the case of robots with finite but very large joint stiffness (singularly perturbed model). The problem of computing nominal torques that produce a desired motion (inverse dynamics) is solved, also addressing the critical inclusion of dissipative terms. The elementary case of a single link driven through an elastic joint is used to illustrate some basic structural properties that are relevant for control design, when link or motor position are taken as system output. Regulation problems are considered for the general case of multi-link manipulators with elastic joints. Solutions are based on a decentralized PD control law with feedback from the motor variables only, completed by constant or on-line gravity compensation terms of increasing complexity. Transient performance can be improved if feedback from the full robot state is considered, i.e., measuring motor and link position and velocity. For the interaction of an elastic joint manipulator with the environment, a compliance control law at the end-effector level is presented. The last part of the chapter is devoted to control solutions for trajectory tracking problems, addressed either by means of a feedback linearization approach or by a simpler linear control design.