In this chapter basic criteria for the design and implementation of interaction control of robotic machines for motor therapy have been briefly introduced and two bio-inspired compliance control laws developed by the authors to address requirements coming from this specific application field have been presented. The two control laws are named the coactivation-based compliance control in the joint space and the torque-dependent compliance control in the joint space, respectively. They try to overcome limitations of the traditional interaction control by taking inspiration from biological motor control, with particular attention to the mechanisms of visco-elastic regulation of the human arm. They basically differ for the strategy of stiffness regulation used to generate a variable proportional gain in the PD control. The control has been designed to ensure a high level of adaptability to different patient motor capabilities and guarantee the maximum level of safety in the interaction. However, also requirements coming from the theory of robot control, such as simplicity of implementation, low computational burden and functional force regulation have been taken into account. In order to carry out a preliminary evaluation of control performance, a simulation tool has been purposely developed in MATLAB/Simulink. It allows simulating the dynamics of the MIT-Manus rehabilitation robot coupled with a human arm. Trials of robot positioning in the free space and in the constrained space have revealed similar performance of the control laws as regards position regulation. However, for force regulation in presence of unexpected constraints the coactivation-based control appears to be less safe than the torque-dependent compliance control, due to the numerous and sharp spikes in the contact/noncontact transitions. This result is enforced by the experimental evidence on a 8-dof robot arm. Based on these preliminary experimental results, the application of the torque-dependent compliance control in the joint space to rehabilitation motor therapy has been simulated. The simulator in fact can be also used to simulate different levels of disability of the patient interacting with the robot. The results showed that also in presence of severe disability the control system is capable of counterbalancing incorrect movements, with an efficacy dependent on tuning the control parameters. Future work will be addressed to further investigate performance of the coactivationbased and torque-dependent compliance control by implementing the two control laws on a real operational robotic machine for motor therapy (e.g. the MIT-Manus system) and carrying out clinical trials. Also, the formulation of the control law in the joint space ensures an easy portability of the control law to exoskeletal systems. Thus, an extension and application of the two compliance controls to these types of machines is envisaged in the near future.