Unlike conventional robotic manipulators, continuum manipulators are inspired by invertebrate structures found in nature, such as octopus arms and elephant trunks. The shape of a continuum manipulator can continuously deform via changing the controllable degrees of freedom, such as bending, extending/contracting, and torsional turning of the arm sections. The manipulator is also passively compliant due to their infinite number of passive degrees of freedom. Hence, continuum manipulators are very flexible and particularly suitable for performing tasks in cluttered environments. Although different mechanical designs have been proposed and validated by teleoperations. There is a great need to study autonomous manipulation of a continuum manipulator.This dissertation addresses research issues in autonomous manipulation using continuum manipulators and introduces novel algorithms, including those for collision detection, whole arm continuum grasping, task constrained manipulation, and continuum manipulation in cluttered, unknown environments. Implementation and testing results are presented to validate the effectiveness of introduced approaches.