  Continuum and soft robots can positively impact diverse sectors, from
biomedical applications to marine and space exploration, thanks to their
potential to adaptively interact with unstructured environments. However, the
complex mechanics exhibited by these robots pose diverse challenges in modeling
and control. Reduced order continuum mechanical models based on rod theories
have emerged as a promising framework, striking a balance between accurately
capturing deformations of slender bodies and computational efficiency. This
review paper explores rod-based models and control strategies for continuum and
soft robots. In particular, it summarizes the mathematical background
underlying the four main rod theories applied in soft robotics. Then, it
categorizes the literature on rod models applied to continuum and soft robots
based on deformation classes, actuation technology, or robot type. Finally, it
reviews recent model-based and learning-based control strategies leveraging rod
models. The comprehensive review includes a critical discussion of the trends,
advantages, limits, and possible future developments of rod models. This paper
could guide researchers intending to simulate and control new soft robots and
provide feedback to the design and manufacturing community.
