Designing the layouts and simulating the assembly of cables are based on flexible cable modeling technology. In this paper, we review the methods used to model deformable cable-like objects. At present, the physical models of one-dimensional cable-like flexible objects are mostly elastic. There are different types of models, which we can classify as mass–spring, multi-body, elastic rod, dynamic spline, finite element models, and so forth. There are a number of significant issues, such as how to couple these models in an appropriate way, take more physical behaviors into account, and develop a more sophisticated/comprehensive model. Some researchers have also studied how to model plastic cables, thin viscous threads, and branched cables; however, those issues are far from fully resolved and need to be studied further. Furthermore, we believe that in future research it will be important to model the cross-sections of cables with different or deformable shapes and complex internal structures, and consider the influence of temperature and alternating stress. •The physical models of deformable cable-like linear objects are summarized.•Some more complex issues are introduced and discussed.•Some opinions on the future research directions are put forward.