We present an integrated approach that provides compliant control of an iCub humanoid robot and adaptive reaching, grasping, navigating and co-manipulating capabilities. We use state-dependent dynamical systems (DS) to (i) coordinate and drive the robots hands (in both position and orientation) to grasp an object using an intermediate virtual object, and (ii) drive the robot's base while walking/navigating. The use of DS as motion generators allows us to adapt smoothly as the object moves and to re-plan on-line motion of the arms and body to reach the object's new location. The desired motion generated by the DS are used in combination with a whole-body compliant control strategy that absorbs perturbations while walking and offers compliant behaviors for grasping and manipulation tasks. Further, the desired dynamics for the arm and body can be learned from demonstrations. By integrating these components, we achieve unprecedented adaptive behaviors for whole body manipulation. We showcase this in simulations and real-world experiments where iCub robots (i) walk-to-grasp objects, (ii) follow a human (or another iCub) through interaction and (iii) learn to navigate or comanipulate an object from human guided demonstrations; whilst being robust to changing targets and perturbations.