Dexterous robotic manipulation of complex nonrigid objects is a requirement for automating many delicate tasks. This work explores various sensing and modeling strategies for tracking the 3D shape of objects during manipulation, allowing for more accurate and responsive planning and control of robotic manipulators. These approaches are evaluated in terms of their ability to correctly capture the behaviour of non-rigid objects as well as their computational complexity, which is strongly constrained by the need for real-time control on robotic platforms with limited computing power.