  Deformable object manipulation (DOM) for robots has a wide range of
applications in various fields such as industrial, service and health care
sectors. However, compared to manipulation of rigid objects, DOM poses
significant challenges for robotic perception, modeling and manipulation, due
to the infinite dimensionality of the state space of deformable objects (DOs)
and the complexity of their dynamics. The development of computer graphics and
machine learning has enabled novel techniques for DOM. These techniques, based
on data-driven paradigms, can address some of the challenges that analytical
approaches of DOM face. However, some existing reviews do not include all
aspects of DOM, and some previous reviews do not summarize data-driven
approaches adequately. In this article, we survey more than 150 relevant
studies (data-driven approaches mainly) and summarize recent advances, open
challenges, and new frontiers for aspects of perception, modeling and
manipulation for DOs. Particularly, we summarize initial progress made by Large
Language Models (LLMs) in robotic manipulation, and indicates some valuable
directions for further research. We believe that integrating data-driven
approaches and analytical approaches can provide viable solutions to open
challenges of DOM.
