The present review focuses on the theoretical model developments made in floating flexible net fish cages and the floating bodies application to offshore aquaculture. A brief discussion of the essential mathematical equations related to various theoretical models of flexible net cages in the frequency domain is presented. The single and array of floating or submerged flexible net cages connected with or without mooring lines are discussed. Further, as the combined effect of the hydroelastic behaviour of floaters and the flexible behaviour of fish cages are necessary to assess their efficiency and survivability from structural damages, the issues and the knowledge gap between the recent and future models are also discussed. In conclusion, the practical suggestions concerning advancements in future research and directions within floating flexible net cages and the hydroelastic response of elastic floaters are highlighted.