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Insects are the most successful group of living things in terms of the number of species, the biomass and their distribution. Entomological research has revealed that the insect sensory systems are crucial for their success. Compared to human brains, the insect central nerve systems are extremely primitive and simple, both structurally and functionally, and are of minimal learning ability. Faced with these constraints, insects have evolved a set of extremely effective sensory systems that are structurally simple, functionally versatile and powerful, and highly distributed, as well as noise and fault tolerant. As a result, in recent years insect sensory systems have been inspirational to new communications and computing paradigms, which have lead to significant advances. However, we believe that the potential for insect-inspired solutions for communications and computing is far from being fully recognized. In particular, the contrasting similarity between the ubiquitous existences of insect sensory networks in nature and the idea of pervasive computing has received little attention. For example, the chemosensory communication systems in many of the moth, ant and beetle populations are essentially ''wireless'' sensory networks. The difference between the ''wireless'' network of an insect population and an engineered wireless sensor network is that insects encode messages with semiochemicals (also known as infochemicals) rather than with radio frequencies; in addition, the computing node is the individual insect powered by its brain, sensory and neuromotor systems, rather than a microchip-powered sensor. The objectives of this paper are threefold: (1) to introduce the state-of-the art research in insect sensory systems from entomological perspectives; (2) to propose potential new research problems inspired by insect sensory system with focusing on unexplored fields; and (3) to justify how and why insect sensory systems may inspire novel computing and communications paradigms.