Particle swarm optimization has captivated the scientific community for three decades. Its effectiveness and efficiency have made it a significant metaheuristic approach in various scientific fields dealing with complex optimization problems. Its simplicity makes it accessible to nonexpert researchers, while its flexible operators and the ease of integrating new procedures allow its application to a wide range of problems with diverse characteristics. Additionally, its inherent decentralized nature facilitates easy parallelization, enabling it to leverage modern high-performance computing systems, effectively. The present work introduces the basic concepts of particle swarm optimization and presents several popular variants that have opened new research directions by incorporating novel ideas into the original algorithm. The focus is on conveying the essential information of these algorithms rather than delving into all the details. A comprehensive list of references and sources is provided for further inquiry, making this text a valuable starting point for researchers interested in the development and application of particle swarm optimization and its variants.