Beyond simple walking, bipedalism implies more generally a capability of manipulation with the feet (pedipulation), through discontinuous deformation of the standing region and continuous manipulation of the reaction forces within the standing region. In this talk, I will present "Dynamics Morphing", a control design paradigm which enables seamless transitions between regulatory and oscillatory behaviors. This paradigm can be used to design globally stable controllers by shaping the system dynamics, while considering both continuous and discontinuous dynamics. I will present various non-time-slaved bipedal motions generated by this approach in a computer simulation.