Swarm intelligence-based optimisation algorithms, inspired by the collective intelligent behaviours of biology groups, have been widely recognised as efficient optimisers for many complex problems, e.g., dynamic optimisation problems, large-scale optimisation problems and many-objective optimisation problems. Swarm intelligence-based algorithms are the generic concepts to represent a range of metaheuristics with population-based iterative process, guided random search and parallel processing. This paper conducts an in-depth analysis of universality and difference of existing swarm intelligence-based algorithms. It also provides a systematical survey of some well-known algorithms. In addition, the expected research issues such as theoretical analysis, hybridisation strategy and complex problems optimisation are discussed thoroughly to inspire future study and more extensive applications.