Nature is a great and immense source of inspiration for solving complex problems in the real world. The well-known examples in nature for swarms are bird flocks, fish schools and the colony of social insects. Birds, ants, bees, fireflies, bats, and pigeons are all bringing us various inspirations for swarm intelligence. In 1990s, swarm intelligence algorithms based on ant colony have highly attracted the interest of researchers. During the past two decades, several new algorithms have been developed depending on different intelligent behaviours of natural swarms. This review presents a comprehensive survey of swarm intelligence-based computation algorithms, which are ant colony optimisation, particle swarm optimisation, artificial bee colony, firefly algorithm, bat algorithm, and pigeon inspired optimisation. Future orientations are also discussed thoroughly.