Fish are able to perceive the surrounding weak flow and pressure variations with their mechanosensory lateral line system, which consists of a superficial lateral line for flow velocity detection and a canal lateral line for flow pressure gradient perception. Achieving a better understanding of the flow field perception algorithms of the lateral line can contribute not only to the design of highly sensitive flow sensors, but also to the development of underwater smart skin with good hydrodynamic imaging properties. In this review, we discuss highly sensitive flow-sensing mechanisms for superficial and canal neuromasts and flow field perception algorithms. Artificial lateral line systems with different transduction mechanisms are then described with special emphasis on the recent innovations in the field of polymer-based artificial flow sensors. Finally, we discuss our perspective of the technological challenges faced while improving flow sensitivity, durability, and sensing fusion schemes.