The collective behaviors of animals, from schooling fish to packing wolves and flocking birds, display plenty of fascinating phenomena that result from simple interaction rules among individuals. The emergent intelligent properties of the animal collective behaviors, such as self-organization, robustness, adaptability, and expansibility, have inspired the design of autonomous unmanned swarm systems. This article reviews several typical natural collective behaviors, introduces the origin and connotation of swarm intelligence, gives the application case of animal collective behaviors. On this basis, the article focuses on the forefront of progress and bionic achievements of aerial, ground and marine robotics swarms, illustrating the mapping relationship from biological cooperative mechanisms to cooperative unmanned cluster systems. Finally, considering the significance of Coexisting-Cooperative-Cognitive (Tri-Co) human-machine system, the key technologies to be solved are given as the reference directions for the subsequent exploration.