Traditional aerial manipulation systems were usually composed of rigid-link manipulators attached to an aerial platform, arising several rigidity-related issues such as difficulties of reach, compliant motion, adaptability to object’s shape and pose uncertainties, and safety of human-manipulator interactions, especially in unstructured and confined environments. To address these issues, partially compliant manipulators, composed of rigid links and compliant/flexible joints, were proposed; however, they still suffer from insufficient dexterity and maneuverability. In this article, a new set of compliant aerial manipulators is suggested. For this purpose, the concept of aerial continuum manipulation system (ACMS) is introduced, several conceptual configurations are proposed, and the functionalities of ACMSs for different applications are discussed. Then, the performances of proposed aerial manipulators are compared with conventional aerial manipulators by implementing available benchmarks in the literature. To enhance the comparison, new features with related benchmarks are presented and used for evaluation purposes. In this study, the advantages of ACMSs over their rigid-link counterparts are illustrated and the potential applications of ACMSs are suggested. The open problems such as those related to dynamic coupling and control of ACMSs are also highlighted.