Motion perception is a critical capability determining a variety of aspects of insects' life, including avoiding predators, foraging, and so forth. A good number of motion detectors have been identified in the insects' visual pathways. Computational modeling of these motion detectors has not only been providing effective solutions to artificial intelligence, but also benefiting the understanding of complicated biological visual systems. These biological mechanisms through millions of years of evolutionary development will have formed solid modules for constructing dynamic vision systems for future intelligent machines. This article reviews the computational motion perception models originating from biological research on insects' visual systems in the literature. These motion perception models or neural networks consist of the looming-sensitive neuronal models of lobula giant movement detectors (LGMDs) in locusts, the translation-sensitive neural systems of direction-selective neurons (DSNs) in fruit flies, bees, and locusts, and the small-target motion detectors (STMDs) in dragonflies and hoverflies. We also review the applications of these models to robots and vehicles. Through these modeling studies, we summarize the methodologies that generate different direction and size selectivity in motion perception. Finally, we discuss multiple systems integration and hardware realization of these bio-inspired motion perception models.