<p>Continuum robots (CRs) have been the subject of intensive researches in recent years because of the wide range of their potential applications. One main domain of application is CR-based grasp, which needs studying grasp taxonomy and grasp synthesis. Despite the importance of these two topics for robotic operations, their concepts for CRs remain to be investigated. The first contribution of this thesis is to present a comprehensive CR-based grasp taxonomy. Grasp taxonomy is a systematic arrangement of space of grasps. For this purpose, different types of CR-based grasp tasks are overviewed. Also, different types of contact shapes between CRs and objects are classified. Finally, existing CR-based grasp configurations in the CR-related literature are compared and classified into a novel taxonomy through a 3-step methodology. Based on this study, nine major grasp families in the field of CRs are introduced, which include 21 sub-grasp types. Then, the taxonomy is enriched by different analyses of CR-based grasp families. Finally, to study the feasibility of the grasp taxonomy, an experimental case of a small-sized CR is investigated. The second contribution of this thesis is to introduce the formulation of CR-based grasp synthesis. Grasp synthesis is the process of determining the CR configuration and contact points on the target object to acquire suitable grasp properties. In this thesis, a synthesis approach relying on an analytical model of CR-based grasp is proposed. The grasp quality measures, which are key to the grasp selection, are formulated based on grasp and CR Jacobian matrices. The Jacobian matrix for CRs is obtained through piecewise constant-curvature modeling and by Cosserat rod-based models, each providing certain advantages. Besides, to reflect the limited workspace of CRs, a new quantitative grasp quality measure is proposed. Also, two experimental grasp quality measures (i.e., path following error and grasp success rate) are introduced to compare and assess the grasps. Then, the effectiveness of the synthesis algorithms is shown through extensive numerical examples and experiments, using single-segment tendon-driven catheters. Moreover, as a requirement for experimental verifications, an experimental set-up for the automation of CRs is developed in collaboration with other researchers in the lab.</p>