Swarm intelligence algorithms are a subset of the artificial intelligence (AI) field, which is increasing popularity in resolving different optimization problems and has been widely utilized in various applications. In the past decades, numerous swarm intelligence algorithms have been developed, including ant colony optimization (ACO), particle swarm optimization (PSO), artificial fish swarm (AFS), bacterial foraging optimization (BFO), and artificial bee colony (ABC). This review tries to review the most representative swarm intelligence algorithms in chronological order by highlighting the functions and strengths from 127 research literatures. It provides an overview of the various swarm intelligence algorithms and their advanced developments, and briefly provides the description of their successful applications in optimization problems of engineering fields. Finally, opinions and perspectives on the trends and prospects in this relatively new research domain are represented to support future developments.