The grey wolf optimizer (GWO) is a newly developed swarm intelligence-based optimization technique that mimics the social hierarchy and group hunting behavior of grey wolves in nature. Here, a detailed introduction of the GWO algorithm is given, after which, three sets of examples are investigated: first, numerical experiments on four benchmark functions are conducted; second, the GWO is applied to the synthesis of linear arrays with the aim of reducing the peak sidelobe level under various constraints; and finally, the performance of the GWO is further verified on the optimization design of two representative antennas, namely, a dual-band E-shaped patch antenna and a wideband magneto-electric dipole antenna. The results show that the GWO is capable of outperforming or providing very competitive results compared with some well-known metaheuristics such as the genetic algorithm, particle swarm optimization, and differential evolution. Thus, it may serve as a promising candidate for handling electromagnetic problems.