The excellent swimming performances of live fish motivate scientists and engineers around the world to study its swimming mechanism and develop fish-like underwater robots, namely, the biomimetic robotic fishes. This paper compares different designs of biomimetic robotic fishes performing Body and/or Caudal Fin (BCF) swimming locomotion, and stresses how the designs evolve. The general trend is to utilize a simpler and more robust mechanism to make biomimetic robotic fishes mimic their counterparts in nature better, at the same time, to exhibit better swimming performances. Representative studies are given and discussed. Challenges of current studies are summarized and future research directions are presented. With state-of-the-art engineering and biological technologies, the biomimetic robotic fishes have great potentials in some areas where the conventional screw propellers are not applicable, like narrow space navigation and eco-friendly environment monitoring.