At present, single-fin propulsion modes, such as pectoral fins and caudal fins, cannot ensure the mobility and forward speed of bionic robotic fish, whereas a multi-fin and flexible body can better ensure a high propulsion efficiency – particularly with low-speed mobility and high-speed stability. Therefore, the cooperative propulsion mode of the pectoral fin and caudal fin has become a research hotspot in recent years. This paper systematically introduces various actuators of robotic fish, including traditional actuators and functional materials. The functional materials include shape-memory alloy wires, ionic polymer–metal composites and piezoelectric ceramics, and their performance characteristics and limitations are discussed. Functional materials can reduce the volume and weight of a robot and reduce noise. Underwater robots have the advantages of flexibility and the ability to perform complex motions. Therefore, flexible robotic fish that combine the flexible behaviour of real fish with robot technology are gradually emerging. Finally, future research directions for bionic robotic fish are presented.