Continuum robots provide inherent structural compliance with high dexterity to access the surgical target sites along tortuous anatomical paths under constrained environments and enable to perform complex and delicate operations through small incisions in minimally invasive surgery. These advantages enable their broad applications with minimal trauma and make challenging clinical procedures possible with miniaturized instrumentation and high curvilinear access capabilities. However, their inherent deformable designs make it difficult to realize 3-D intraoperative real-time shape sensing to accurately model their shape. Solutions to this limitation can lead themselves to further develop closely associated techniques of closed-loop control, path planning, human-robot interaction, and surgical manipulation safety concerns in minimally invasive surgery. Although extensive model-based research that relies on kinematics and mechanics has been performed, accurate shape sensing of continuum robots remains challenging, particularly in cases of unknown and dynamic payloads. This survey investigates the recent advances in alternative emerging techniques for 3-D shape sensing in this field and focuses on the following categories: fiber-optic-sensor-based, electromagnetic-tracking-based, and intraoperative imaging modality-based shape-reconstruction methods. The limitations of existing technologies and prospects of new technologies are also discussed.