In robotics, particularly for autonomous navigation and human-robot collaboration, the significance of unconventional imaging techniques and efficient data processing capabilities is paramount. The unstructured environments encountered by robots, coupled with complex missions assigned to them, present numerous challenges necessitating diverse visual functionalities, and consequently, the development of multifunctional robotic vision systems has become indispensable. Meanwhile, rich diversity inherent in animal vision systems, honed over evolutionary epochs to meet their survival demands across varied habitats, serves as a profound source of inspirations. Here, recent advancements in multifunctional robotic vision systems drawing inspiration from natural ocular structures and their visual perception mechanisms are delineated. First, unique imaging functionalities of natural eyes across terrestrial, aerial, and aquatic habitats and visual signal processing mechanism of humans are explored. Then, designs and functionalities of bio-inspired electronic eyes are explored, engineered to mimic key components and underlying optical principles of natural eyes. Furthermore, neuromorphic image sensors are discussed, emulating functional properties of synapses, neurons, and retinas and thereby enhancing accuracy and efficiency of robotic vision tasks. Next, integration examples of electronic eyes with mobile robotic/biological systems are introduced. Finally, a forward-looking outlook on the development of bio-inspired electronic eyes and neuromorphic image sensors is provided.